Fracture Toughness KIC Research Articles

The Minimum Energy Density Criterion for the Competition between Shear and Flat Fracture

It is generally recognized that the fracture toughness KIC of materials represents the crack resistance during fracture, i.e., the energy consumption. In this study, AISI 4340 steels with different strength are applied to systematically investigate the intrinsic mechanism of fracture toughness. It is found that the fracture surface morphologies of AISI 4340 steels change from quasi‐cleavage fracture to dimple fracture with increasing the tempering temperature. While, the specimen size has almost no effect on the fracture mechanism of shear/flat fracture region, demonstrating that the fracture toughness depends on the proportion of shear and flat fracture region. Additionally, the shear lip width of the KIC specimen will increase to a constant value with enhancing the specimen thickness. Based on the energy balance principle, the maximum shear lip width can be obtained at the minimum fracture energy density of materials; consequently, there is an essential relationship between the shear fracture and fracture toughness, i.e., the minimum energy density criterion. The new finding, which provides a scaling law to well evaluate the plane strain fracture toughness of new materials with high toughness (e.g., nanostructured materials and metallic glasses), may broad the understandings on the fracture toughness.

Fracture toughness of synthesised high-performance epoxies subject to accelerated water aging

The effects of water uptake on the fracture toughness of epoxy systems with high glass-transition temperatures (Tg above 170 °C) are investigated. Aging conditioning has been conducted in hot water, followed by a desorption conditioning in a room temperature dry-airborne. Water aging determines plasticisation effects and crosslink-density modifications, revealed by reductions of the Tg. It is less known how such modifications influence the material fracture toughness. In this study, Single Edge Notched Bending samples have been tested according to standards, to evaluate the KIC fracture toughness at different stages of water absorption-desorption. The characterisation has been supported by Photoelastic Stress Analysis, allowing to evaluate stresses induced by swelling during aging. Results indicate that swelling stresses activate a crack closure mechanism that might contribute to the observed increase of the measured fracture toughness during water absorption, but are ineffective at saturation. Two epoxy systems, one based on DGEBA and the other on DGEBF, having different cross-link densities, have been studied. The plasticisation achieved at saturation translated into a significant increase of fracture toughness only in DGEBA, while fracture toughness measured at other conditioning stages was likely influenced by internal swelling stresses and sample pre-cracking strategy.

Measurement uncertainty of plane-strain fracture toughness KIC testing by the Monte Carlo Method

Abstract The reliable determination of materials' mechanical properties is a fundamental factor for their application in engineering, and the estimation of the measurement uncertainty in testing laboratories has a direct impact on the interpretation of the results. Recent literature demonstrates that one of the most widely used methodologies for uncertainty estimation, the Guide to the Expression of Uncertainty in Measurement (GUM), has limitations, especially in cases where the mathematical model has a high degree of non-linearity. Furthermore, it makes approximations for the final probability distribution. In these cases, it is recommended that the measurement uncertainty is determined by the Monte Carlo Method (MCM), which considers the propagation of the distribution rather than the propagation of uncertainties. Thus, given the limitations of the GUM method and the importance of estimating the measurement uncertainty of mechanical tests, this work aims to implement the measurement uncertainty estimation for the plane-strain fracture toughness (KIC) test of metallic materials through the Monte Carlo Method. The results of the work confirm the importance of estimating the measurement uncertainty of fracture toughness tests.

Study of fracture toughness and bend test morphologies of HVOF sprayed Cr3C2-25% NiCr coating after heat treatment

Majority of the industrial components are subjected to high temperature exposure, where crack propagation occurs due to shear failure. The paper involves the study of the fracture toughness of heat treated Cr3C2-NiCr coating at three different service temperatures (750°C, 850°C, and 950°C for 1-hour aging) using indentation techniques to measure the crack resistance of the coating. At 750°C and 850°C, the coating cracked at the bend area, but not spalled. At 950°C, the coating spalled and delaminated from the substrate indicating poor adhesion after prolonged exposure. The influence of heat treatment on the fracture toughness and adhesion properties of the Cr3C2-25%NiCr coating were also investigated. The high temperature exposure at 950°C, resulted in a shear failure of the coating due to the presence of splat contraction. The increase in temperature increases the fracture toughness KIC of the coating, with the decrease in hardness. It was observed that the oxidation levels enhanced on the top layer of the coating, which acted like a core region for crack initiation at 950°C resulting in shear failure during bend test.

Calculation of Mechanical Fracture Parameters of Chevron Notched Core Based Concrete Specimen: Software <i>CheF</i>

The structural concrete can be also characterized via parameters obtained by evaluation of fracture tests. Therefore, this paper presents software CheF developed in Java programming language, designed for evaluation of three-point bending fracture tests of core based concrete specimens with chevron type notch. The records of fracture tests in form load vs. displacement and load vs. crack mouth opening displacement diagrams are analysed by software CheF to obtain values of selected mechanical fracture parameters: modulus of elasticity E, fracture toughness KIc, and fracture energy GF, determined based on the linear elastic fracture mechanics approach and work-of-fracture method.

一种岩石I型断裂韧度K<sub>Ic</sub>估算方法

岩石的I型断裂韧度KIc是表征岩石材料抵抗裂纹失稳扩展即脆断破坏的力学性能指标，而在实验室开展该参数的测试工作往往比较困难。为此，本文基于岩石单轴抗拉强度等效的原则，结合岩石I型断裂韧度与单轴抗拉强度、岩石Hoek-Brown (H-B)强度准则的经验参数mi与单轴抗压和抗拉强度之间的相关关系，提出以岩石单轴抗压强度和参数mi估算岩石I型断裂韧度KIc的经验公式。最后，通过相关试验成果验证了经验公式的可靠性。在缺乏必要的试验数据时，所建议的经验关系式可用于通过岩石单轴抗压强度对I型断裂韧度的初步估算。 The mode I fracture toughness KIc of rocks is a mechanical properties index which characterizes the resistance of instability expansion of inner cracks, namely brittle fracture damages of materials, but it is usually difficult to obtain this parameter in laboratory test. Therefore, based on the equivalent principle of uniaxial tensile strength of rocks, combining the relationship between mode I fracture toughness KIc and tensile strength of rocks with the relationship between experience parameter mi of Hoek-Brown (H-B) strength criterion and uniaxial compressive, tensile strength of rocks, a new estimation method of mode I fracture toughness KIc of rocks based on uniaxial compressive strength and experience parameter mi of rocks is proposed. Lastly, the reliability of the correlation is validated by some related testing results. When the basic testing data are unavailable, the proposed correlation can provide a preliminary estimation value of mode I fracture toughness KIc by the uniaxial compressive strength of rocks.

Tomographic investigation of the fracture toughness of the quasi-brittle specimens subjected to four-point bending test

It is well known that detailed investigation of fracture mechanics of the quasi-brittle materials is rather complicated task as standard loading devices do not allow to interrupt loading test after reaching maximal loading force. The reason is that the point of maximal loading force is followed by the evolution of the fracture processes, due to elastic energy stored in the loading device itself. This fundamental obstacle was overcome in this work thanks to a newly developed compact four-point bending device. We show that shape of the crack can be evaluated on the basis of the so called differential tomography, which compares reference and actual states of the loaded specimen. Similarly, it is possible to evaluate displacement and strain fields by analyzing the series of loading states using the digital image correlation tools. Using such a methodology, local fracture toughness KIc is calculated thanks to information about of the crack path and evaluated CTOD parameter.

Improved mechanical properties of dense β-Si3N4 ceramics fabricated by spark plasma sintering with Al2O3-YSZ additives

In this work the influence of sintering conditions on structure and mechanical properties of Si3N4 ceramics was investigated. Nearly full dense ?-Si3N4 ceramics with excellent mechanical properties and interlock microstructure of elongated grains was fabricated using Al2O3 and yttria-stabilized zirconia (YSZ with 3mol% Y2O3) as sintering additives by spark plasma sintering (SPS) at relatively low temperature of 1600?C for 15min. X-ray diffraction analysis shows that the SPSed sample is pure ?-Si3N4 phase without any secondary crystalline phase. The elements Al, Zr, Y and O of the additive can diffuse into Si3N4 lattice forming ?-Si3N4- based solid solution. The residual additive formed an amorphous phase at the ?-Si3N4 grain boundaries. The ?-Si3N4 ceramics obtained by SPS using 6.0wt.% Al2O3 and 6.0 wt.% YSZ as additives shows interlock elongated ?-Si3N4 grains of 500 nm in width and 3000 nm in length, high density of 3.29 g/cm3, Vickers hardness of 16.15GPa and high fracture toughness KIC of 6.75MPam1/2.

Prediction of ceramic fracture with normal distribution pertinent to grain size

Fracture of brittle ceramics initiated from shallow surface cracks comparable to their average grain sizes (G) can fluctuate significantly. Such fluctuations can contain crucial information on the inherent relations between the average grain size G and bulk ceramic properties such as the tensile strength ft and fracture toughness KIC. It was proposed in this study that the characteristic crack a*ch = 0.25(KIC/ft)2 = constant × G, inspired by observations of strength distributions with different a*ch/G ratios. It was found that normal distributions with the smallest standard deviation exist around a*ch = (2.5–3.5) × G, based on quasi-brittle fracture results of four different ceramics with G from 2 to 20 μm and shallow surface cracks from 100 nm to 650 μm. Using the average value of the relative characteristic crack a*ch/G ≈ 3, the mean and standard deviation (σ) were determined by normal distributions for both the tensile strength ft and fracture toughness KIC. Quasi-brittle fracture of those fine-grained ceramics based on the mean values and standard deviations was thus predicted. The upper and lower bounds with 96% reliability (±2σ) specified by the normal distributions covered nearly all experimental data ranging from the strength-controlled to toughness-controlled asymptotic limits, and quasi-brittle fracture between the two. With the knowledge of the average grain size G, the tensile strength ft becomes the sole parameter required to describe the entire fracture range.

Fracture toughness and structural evolution in the TiAlN system upon annealing

Hard coatings used to protect engineering components from external loads and harsh environments should ideally be strong and tough. Here we study the fracture toughness, KIC, of Ti1−xAlxN upon annealing by employing micro-fracture experiments on freestanding films. We found that KIC increases by about 11% when annealing the samples at 900 °C, because the decomposition of the supersaturated matrix leads to the formation of nanometer-sized domains, precipitation of hexagonal-structured B4 AlN (with their significantly larger specific volume), formation of stacking faults, and nano-twins. In contrast, for TiN, where no decomposition processes and formation of nanometer-sized domains can be initiated by an annealing treatment, the fracture toughness KIC remains roughly constant when annealed above the film deposition temperature. As the increase in KIC found for Ti1−xAlxN upon annealing is within statistical errors, we carried out complementary cube corner nanoindentation experiments, which clearly show reduced (or even impeded) crack formation for annealed Ti1−xAlxN as compared with their as-deposited counterpart. The ability of Ti1−xAlxN to maintain and even increase the fracture toughness up to high temperatures in combination with the concomitant age hardening effects and excellent oxidation resistance contributes to the success of this type of coatings.

A non-local probabilistic method for modeling of crack propagation

Damage process in engineering systems is strongly affected by spatial heterogeneity and local discontinuities in the materials, which are significantly influencing the reliability and integrity of the systems. In this paper, we present a new stochastic approach as a tool for performing uncertainty quantification in simulating damage evolution in heterogeneous brittle materials. One of the advantages of the proposed method is its ability to capture the influence of uncertainty in the mechanical properties of whole simulation domain, not just the properties of the immediate neighbourhood around the crack tip, on direction of crack propagation. In fact, through this approach the direction of crack propagation at a specified point of localised damage can be probabilistically determined based on nonlocal mechanics theory, in which the influence of local discontinuities and weak points located at further distances from the crack tip, in addition to those located at the immediate neighbourhood of the local damage, are incorporated into the model. The reliability and performance of the methodology are examined through simulation of numerical examples and comparison with analytical results and experimental data. The case studies show how the crack initiation angle can be reasonably estimated with this methodology and how this approach provides realistic values of fracture toughness KIC and fracture energy Gf.

Annealing effect on the fracture toughness of CrN/TiN superlattices

Superlattice films are generally known for their exceptional high hardness compared to their monolithic constituents. Recently, we have shown that CrN/TiN superlattice films exhibit a peak in fracture toughness for a bilayer period of 6.0nm, similar to the former reported peak in hardness. We propose that a dominating factor for obtaining such favourable material properties is the interface constitution between the individual layers.To proof this notion, we have intentionally modified the interface sharpness by post-deposition vacuum annealing of the samples at different temperatures. This promotes interdiffusion of Ti or Cr into its adjacent layers and gradually changes the interfaces to interphases (because TiN and CrN form a solid solution). In order to obtain reliable KIC fracture toughness values as a function of the annealing temperature, in-situ micromechanical cantilever bending tests on ex-situ vacuum annealed freestanding films were performed. High temperature loads take also place during machining processes like dry cutting or high-speed cutting, and are thus of high practical relevance.

Microcellular PP/GF composites: Morphological, mechanical and fracture characterization

The aim of the present work is to analyze the morphology, mechanical properties and fracture behaviour of solid and foamed plates made of glass fiber-reinforced PP. The morphology exhibited a solid skin/foamed core structure, dependent on the foaming ratio. Simulation of the microcellular injection molding process with Moldex 3D® software provided a good approach to the experimental results. The flexural properties and impact resistance showed lower values as the apparent density decreased, but constant specific properties. The fracture characterization was carried out by determining the Crack Tip Opening Displacement (CTOD) at low strain rate, as well as the fracture toughness (KIc) at impact loading. Foamed specimens presented higher values of CTOD than the solid ones and higher as the foaming ratio increases, due to cells acting as crack arrestors by blunting the crack tip. However, the fracture toughness KIc decreased with decreasing the apparent density. Anisotropy due to fiber orientation was also observed. Fibers were aligned in the filling direction in the surface layers, while they were oriented in the transverse direction in the core. According to the amount of fibers oriented in one direction or another, different properties were obtained.

A temperature-dependent model for predicting the fracture toughness of superalloys at elevated temperature

The plane-strain fracture toughness of tensile mode KIC of superalloys at elevated temperature plays an imperative role in damage tolerance design and structure integrity assessment. In this paper, a novel temperature-dependent model is proposed to predict KIC values of superalloys at elevated temperatures, which is based on stress–strain curves and linear expansion coefficients α of superalloys. Firstly, relation between KIC and strain-hardening exponent n, Young’s modulus E is introduced based on Krafft’s model. Then, relation between n and temperature is established by a semi-empirical method, and relation between E and temperature is derived based on physical meanings. To validate the model, KIC measurement tests on standard specimens made from turbine disc Nickel-based superalloy GH4720Li are conducted under temperatures of 25 °C, 300 °C, 550 °C, 600 °C, and 650 °C, respectively. Tested results of GH4720Li show that the maximum error between the predicted values of KIC and tested ones is within 10% under all temperatures. Tested KIC results of another superalloy GH4169 (High temperature materials session of China metal institute, 2012) also agree well with the predicted ones of the model. The model can be used to design high temperature components based on damage tolerance design concept.

Fracture behavior of nuclear graphite under three-point bending tests

Three-point bending tests are performed on center-notched graphite beams to study the fracture properties of IG11 graphite. Electronic speckle pattern interferometry (ESPI) is used to measure the full-field deformation of the graphite beams. A clip gauge is used to measure the crack mouth opening displacement (CMOD) of the beams, which validates the ESPI measurements. In addition, finite element (FE) analysis is performed by using the ABAQUS code coupled with the extended FE method to simulate the growth of cracks in graphite. A combined stress-energy based fracture criterion, specifically, damage for traction separation laws based on maximum principal stress damage initiation and energy based damage evolution with linear softening is applied. The numerical results are compared with the experimental results which show exceptional agreement, thus confirming the accuracy of the FE model. The fracture toughness KIc, fracture energy GF, peak load Pmax and critical displacements at the peak load of each specimen are determined. From the displacement contours measured by ESPI, the positions of the neutral axis and crack opening displacement (COD) profiles at different loading levels are estimated. From the phase maps, the changes in the fracture process zone (FPZ) are analyzed and the size of the FPZ is determined. The strain contours at different loadings indicate that the material near the crack tip experiences biaxial tensile stress.

Fracture investigation of V-notch made of tungsten-copper functionally graded materials

The fracture of V-notches with end holes made of tungsten-copper functionally graded material under mode I has been studied in this paper. The averaged strain energy density over a well-defined control volume was employed to predict the fracture loads. A numerical approach was used to determine the outer boundary of the control volume. Mechanical properties such as elasticity modulus, Poisson’s ratio, fracture toughness KIc, and ultimate tensile stress have been considered to obey the power law function through the specimen width.

Wedge-splitting tests for tensile strength and fracture toughness of concrete

This study presents a new approach for determination of tensile strength ft and fracture toughness KIC of concrete using wedge-splitting (WS) specimens as neither property can be easily measured because of the heterogeneous material structures. The Boundary Effect Model (BEM) was extended to WS geometry and relevant equations were derived so that more concrete properties can be determined by the load and displacement measurements. The new model considers the influence of coarse aggregate structures on concrete fracture by linking the fictitious crack growth Δafic at peak load Pmax to the maximum aggregate size dmax. The random aggregate distribution and inevitable variations in Δafic and Pmax are considered by a discrete number β. WS results of concrete specimens with dmax from 10mm to 25mm and specimen size W from 150mm to 1200mm reported in literature are analyzed for a range of β from around 0.2 to 2.0. It is found that on average β≈1 is a good approximation for common WS specimens with W/dmax<20. Then reliable ft and KIC, which is the asymptotic limit for a large structure with a long crack, can be obtained, regardless whether WS specimens are geometrically similar, or have the same size but different notch lengths. Finally, it is concluded that quasi-brittle fracture of concrete is fully predicted if both KIC and ft are known.

Structure and properties of superhard materials based on aluminum dodecaboride α-AlB12

The structures and mechanical properties of materials based on α-AlB12 without additives and with additions of carbon and titanium carbide sintered under high (2 GPa) pressure and by hot pressing (30 MPa) in the contact with hexagonal BN. The light materials were obtained having high hardness, fracture toughness, ultimate strengths at bending, R bm , and compression. The addition of 17 wt % C to α-AlB12 and sintering at 30 MPa makes possible to achieve fracture toughness KIc (49 N) = 5.9 ± 1.4 MPa·m0.5, hardness H V (49 N) = 23.6 ± 2.8 GPa, bending R bm = 310 MPa and compression R cs = 423 MPa strengths and specific weight was γ = 2.7 g/cm3. The addition of 20 wt % TiC to α-AlB12 and sintering at 30 MPa resulted in the formation of AlB12C2 and TiB2, increase of the hardness H V (49 N) = 28.9 ± 1.9 GPa, R bm = 633 MPa, R cs = 640 MPa and γ = 3.2 g/cm3, the KIc(49 N) = 5.2 ± 1.5 MPa·m0.5.

Fracture of 0.1 and 2 m long mortar beams under three-point-bending

Two hugely different mortar beams with the volume ratio close to 1:1000 were tested under three-point-bending (3-p-b) to verify fracture predictions for the large and long (LL) structures from results of the small and short (SS) specimens. They differed by both size and geometry: SS specimens with span length S=0.1m, width W=40mm and S/W=2.5, and LL beams with S=2m, W=500mm and S/W=4. This study performed and analysed quasi-brittle fracture of 0.1m SS specimens with initial notch a0 from 1 to 25mm for determination of tensile strength ft and fracture toughness KIC, from which fracture of 2m LL beams with a0 of 250mm was accurately predicted. Experiment results from the two vastly different 3-p-b beams, highly heterogeneous SS and nearly homogeneous LL in comparison to aggregates, were analysed by the boundary effect model (BEM).

Effects of nano mechanical properties on LiNbO3 fixed abrasive lapping

ABSTRACTThe nano mechanical properties of brittle materials are the key factors affecting nano machining performance. Lithium niobate (LN) single crystal is the typical anisotropic brittle material. The hardness H and crack length of LN crystals on X-cut wafers were measured through indentation experiments, and the fracture toughness KIC and the critical cutting depth dc along <001> orientations were estimated. A set of fixed-abrasive (FA) lapping pads mixed with diamond grains of different sizes were prepared for lapping on X-cut wafers. The effects of abrasive cutting depth δ and dc on material removal rate (MRR) and surface roughness were discussed. Results indicate that: the surface hardness H of X-cut is about 6 GPa. And the minimum KIC and dc on X-cut are 0.67 MPa.m1/2 and 63.6 nm (along <001> orientation), respectively. Lapping tests show that when the abrasive cutting depth δ exceed the dc, MRR will increase significantly, accompanied with brittle material removal and low surface quality.