The effect of residual stresses on brittle and ductile fracture initiation predicted by micromechanical models

The effect of a realistic residual stress field on the predicted initiation of brittle and ductile fracture in a pressure and axially loaded circumferentially cracked pipe is examined using finite element analysis, micromechanical models of fracture initiation, andJ-Q theory. The study confirms that residual stresses contribute to the driving force and reduce fracture loads early in the loading history. In addition, results show that the residual stresses severely alter theJ-value (i.e., fracture toughness) predicted for the onset of brittle fracture. The reason for this decrease is found to be the increase in constraint generated by the residual stress field. In contrast, the effect of residual stresses on the ductile fracture initiation toughness is shown to be negligible. kw]Key words kw]residual stress kw]fracture initiation kw]micromechanics     

Influence of whisker toughening and microstructure on the wear behavior of Si3N4- and Al2O3-matrix composites reinforced with SiC

A comparative study of the influence of randomly-oriented SiC whiskers on the abrasive wear behavior of several commercially-produced Si₃N₄- and Al₂O₃-based ceramics suggested that the residual stress states present within the materials can be important in predicting their wear resistance. The addition of SiC whiskers to the Si₃N₄ matrix created residual tensile stresses at the whisker-matrix interfaces which led to enhanced bulk fracture toughness, but which degraded the fracture toughness at the microstructural level, and thus the abrasive wear resistance, by promoting easier whisker debonding and removal by the abrasive particles. The addition of SiC whiskers to an alumina matrix, on the other hand, led to the creation of residual compressive stresses at whisker-matrix interfaces, producing a locally tougher interface that was more able to withstand the rigors of the abrasive wear environment. These results indicate that in brittle materials, improved bulk mechanical properties do not always translate directly to improved performance in a tribological environment.     

Robust design and manufacturing of ceramic laminates with controlled thermal residual stresses for enhanced toughness

Boron carbide-silicon carbide ceramic composites are very promising armor materials because they are intrinsically very hard. However, their fracture toughness is not very high. Their ballistic performance could be significantly increased if the brittleness of these materials could be decreased. Here we report development of boron carbide-silicon carbide layered ceramics with controlled compressive and tensile stresses in separate layers. Such B₄C-SiC laminates with strong interfaces can provide high apparent fracture toughness and damage tolerance along with high protection capabilities. The theory of heterogeneous layered systems was used to develop optimal design parameters allowing the evaluation and maximization of apparent fracture toughness. The layered composites were designed in a way to achieve high compressive residual stresses in thin B₄C-SiC based layers and low tensile residuals stresses in thick B₄C layers. The residual stresses were controlled by the phase composition of layers and the layers thickness. The estimated apparent fracture toughness was calculated for both three layered and nine layered composites. B₄C-30 wt%SiC/B₄C laminates were made based on the optimized design for high apparent fracture toughness. Processing of laminates involved preprocessing of powders, forming green tapes and hot pressing. Work is in progress to measure fracture toughness of laminates, as well as their strength, hardness and the ballistic performance.     

Residual stress measurements in welded steel beam column connections by scanning acoustic microscopy

Residual stresses which arise from thermal expansion and contraction due to welding may have contributed to the brittle fracture exhibited by welded steel beam-to-column connections during the Northridge Earthquake. These residual stresses have a strong influence on crack initiation and crack propagation in the vicinity of stress concentrations (i.e., unfused backup bar in welded steel beam-to-column connections) and account for changes in the driving force for fracture. They affect material toughness by changing the constraint condition under which fracture occurs. Currently, all methods of dealing with residual stresses are hampered by the lack of a consistent means of measuring the magnitudes and distribution of these stresses. This paper describes a new acoustic microscopy technique that allows the mapping of residual stresses in welded connections with high spatial resolution. The technique is based on the sensitivity of polarized acoustic modes to local elastic anisotropy induced by stress. The technique furthermore allows the mapping of residual stresses in a tomographic way by changing the frequencies of the acoustic waves. The results reveal that the magnitude of the residual stresses is influenced by the local microstructure of the steel and the weld metal. Ductile microstructures within the weld and the heat affected zone release residual stresses by yielding, whereas brittle microstructures retain residual stresses.     

脆性涂层材料断裂韧性和残余应力压痕表征技术综述

多种多样的脆性涂层材料已成为航天航空、国防科技领域的核心关键材料,在国民经济中发挥了巨大作用。断裂韧性和残余应力是评估脆性涂层材料的重要力学性能指标。维氏压痕法是表征脆性涂层材料体系力学性能指标的有效方法之一,得到了广泛的应用。从涂层特点、压痕测试方法、力学模型、实验装备等方面综述了脆性涂层断裂韧性和残余应力压痕测试的研究进展,讨论了力学模型的特点和适用性,并对今后脆性涂层材料压痕表征研究进行了分析展望。     

Vickers Indentation Fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings

For massive brittle materials, the fracture toughness in mode I, K_IC, can be determined using various reliable techniques. Besides, Vickers Indentation Fracture (VIF) technique has been developed to locally determine fracture toughness. However, since the indentation test generates a complex three-dimensional crack system around the indent, fracture toughness, K_C, is calculated instead of K_IC. Consequently some authors rightly reject the VIF technique to determine standard fracture toughness by arguing that the literature counts numerous VIF crack equations thus revealing discrepancies of this technique. Nevertheless in some cases (e.g. brittle ceramic coatings) inclusive material techniques are not applicable since presence of the substrate and/or multi-crack network can modify the crack propagation into the coating.In this work, we employed VIF technique to study multi-cracking behavior of titania, alumina and zirconia ceramic oxide coatings obtained by plasma spraying. To calculate VIF toughness, we propose (i) to select two crack equations for radial-median and Palmqvist cracking modes respectively, (ii) to adjust the crack equation of Miranzo and Moya for intermediate cracking mode, (iii) to develop a mathematical approach to determine the cracking mode, (iv) to take into account the multi-crack network by defining an equivalent four-crack system and (v) to propose a universal crack equation applicable independently of the cracking mode.     

Festigkeit und Zähigkeit als Sicherheitskriterien im Apparatebau

Strength and Toughness, Criteria of Safety for Construction of Apparata. In the chemical research technique often high requirements are being set on the materials of apparata due to pressure, temperature and corrosive medias. While the strength necessary to avoid macroscopical deformation can be guaranteed today without difficulties, this does not go similarly for the toughness. The toughness of steel being a condition in the strength calculation is the real safety criterion for welded structures. This is especially applicable in the case of local peak stress due to construction or of micro cracks caused during manufacturing or service. If – as mostly in practice – local inhomogeneities and unknown residual stresses are existing, the linear fracture mechanics can only be applied with empirical factors. The best safety even with unforeseen overloadings can be seen in such a toughness, which avoids brittle fracture at all. The possible test methods will in any case have to reliably consider also the heat affected zones of weldings, since brittle cracks also in tough matrix can only be absorbed under limited stresses.     

Correlation of fracture toughness with microstructural features for ultrafine‐grained 6082 Al alloy

In the present work, cryorolling (CR) and room temperature rolling (RTR) followed by annealing (AN) at 200°C were carried out to investigate the effects of grain size, precipitates (Mg‐Si‐phases), and AlFeMnSi‐phases on the fracture toughness of 6082 Al alloy. Using the values of the conditional fracture toughness, (K_Q), in the critical fracture toughness (K_IC) validation criteria, it was found that the sample size is inappropriate, which implies that the conditional fracture toughness obtained cannot be considered as the critical fracture toughness. Therefore, to establish the relative improvement in fracture toughness, the equivalent energy fracture toughness (K_ee) and J‐integral were calculated and used. The results show that the values of K_ee (89.91 MPa √m) and J (89.86 kJ/m²) obtained for the sample processed via CR followed by AN (CR + AN) are the highest when compared with the other samples processed through CR, RTR, and RTR followed by AN, RTR + AN. Microstructural features such as high fraction of low Taylor factor, high fraction of kernel average misorientation, Si‐rich particles, small size AlFeMnSi‐phases, and mixed mode of failure (transgranular shear and micro‐void coalescence) also support the high fracture toughness in the CR + AN sample. It was also observed that the effect of residual stresses on the fracture toughness of CR and RTR samples is minimal. Therefore, the correlation between microstructure and residual stresses is not considered in the present work due to very small values of the residual stresses for CR and RTR samples and the absence of residual stress from the heat‐treated samples.     

The effect of a residual stress field on fracture initiation in RPV steel

Whether flaws in structures containing residual (secondary) stresses will extend under particular operational (primary) loads depends on the extent to which the residual stress field affects: (a) the nature and distribution of initiators; (b) the combined (primary + secondary) stresses and strains experienced by potential initiators. This paper compares fractographic data from specimens loaded by only a primary stress with data from specimens also containing a tensile residual stress field. Three‐dimensional elastic–plastic finite element calculations are used to characterize the stress–strain conditions at the initiation sites at the onset of brittle fracture. The introduction of a residual stress changes the dominant stage in fracture nucleation from microcrack extension to particle cracking. This offsets some of the decrease in fracture toughness expected when the residual stress field increases specimen constraint.     

Anrißerzeugung in WC-Co-Hartmetall-Proben für die Messung des kritischen Spannungsintensitätsfaktors KIC

Precracking of WC-Co-Hardmetal-Specimens for Fracture-Toughness Testing The determination of a valid critical stress intensity factor K_IC requires an extremely sharp, well defined initial crack. Methods producing such a crack are well known for metallic materials, but they often can not be used with brittle materials, like cemented carbides or ceramics. Their low fracture toughness makes a controlled crack growth under pure tensile stress nearly impossible. More useful are precracking methods, utilizing a stress gradient to stop the crack at defined depth. A very simple methods uses the indentation of a hardness tester to produce a semi-elliptical surface crack, interfered with residual stresses. For different areas of application and specimen geometries, bridge indentation, wedge indentation and composite bending method produce cracks with a straight front. Also under cyclic loading, under tensile as well as under compressive stress, the creation of a sharp precrack, applicable in K_IC measurement, is possible.     

Determination of Remnant Residual Stresses in Fracture Toughness Specimens Extracted From Large Components

Abstract: Material fracture toughness data are required to undertake fitness‐for‐service assessments of engineering components containing cracks. Calculations of crack driving force in the component are compared with material fracture toughness values to assess the likelihood of subsequent failure. Experimental measurements of fracture toughness are usually made on small specimens extracted from a larger ‘parent’ component following strict experimental guidelines, formulated to ensure measured toughness values in the fracture specimens are appropriate for use in the full‐size component. Implicit in this procedure is the assumption that the extracted fracture specimens contain no residual stresses, with any residual stresses in the full‐size component being accounted for in the crack driving force calculation. This paper considers a recent conjecture within the structural integrity community that the extracted fracture specimens may themselves contain a residual stress field which may influence measurements of fracture toughness. This could potentially lead to a degree of ‘double accounting’, i.e. the effect of residual stresses may be included in both the material toughness and the crack driving force. This, in turn, could lead to unnecessary conservatism in safety assessments. To explore this conjecture, the results of numerical modelling and neutron diffraction measurements of residual stresses in fracture specimens extracted from two different welded parent components are presented. One of the components is significantly larger than the extracted specimens, with the other being marginally larger than the extracted specimens. Results confirm the intuitive expectation that the residual stresses in specimens extracted from much larger components are negligible, whereas if the dimensions of the extracted specimens are comparable with the larger component then significant residual stresses may remain.     

Preparation, microstructure and mechanical properties of metal-particulate/glass-matrix composites

Composites with a borosilicate glass matrix containing different concentrations of vanadium particles were fabricated by powder metallurgy and hot-pressing. The mechanical properties and fracture behaviour of the composites were assessed by a range of techniques. Young's modulus, fracture strength in bending, and fracture toughness increased with vanadium content. By virtue of the good interfacial bonding and low residual internal stresses, an effective crack-particle interaction during fracture was achieved. The fracture toughness of composites containing 30 vol. % of vanadium inclusions was approximately 65 % higher than that of the unreinforced glass. Experimental values for the fracture toughness increment were in good qualitative agreement with the predictions of theoretical models in the literature. Extensive plastic deformation of the vanadium inclusions was not found, however. This was attributed mainly to the constraint imposed by the rigid matrix surrounding the particles and to possible embrittlement of the particles during composite fabrication at high temperatures. The brittleness index (B) of the composites was calculated and its relevance for characterisation of the ductile versus brittle behaviour of brittle-matrix composites is discussed.     

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.     

Debond coating requirements for brittle matrix composites

The cause of improved fracture toughness in Y₂O₃-coated niobium-toughened TiAl relative to either uncoated niobium or Al₂O₃-coated niobium was examined. Reactively sputtered Y₂O₃ coatings, 1–2 m thick, were deposited on to rock salt (NaCl), polished single-crystal (0001) Al₂O₃, and polished polycrystalline niobium. Sputtered niobium coatings, 1–2 m thick, were also deposited on to polished single-crystal Y₂O₃ substrates for comparison. The oxide coating was characterized and consisted of stoichiometric bcc Y₂O₃ witha ₀=1.0602 nm. Indentation tests were performed to correlate the fracture toughness and debond characteristics of as-deposited Y₂O₃ coatings on Al₂O₃ and polycrystalline niobium, and niobium coatings on single-crystal Y₂O₃, to that found in TiAl/Nb and Al₂O₃/Al₂O₃ laminates. The calculated fracture toughness of sputtered Y₂O₃ on sapphire was similar to reported values for bulk Y₂O₃. However, a wide variation in interfacial fracture toughness was obtained by indentation methods, and is attributed to the microstructure of as-deposited coatings and to weak bonding between as-deposited yttria and the sapphire substrate. These results are related to factors that affect debonding and fracture toughness of brittle matrix composites. Reactive and non-reactive metal/ceramic systems were reviewed in an effort to understand why Y₂O₃ coatings perform well. It is postulated that yttrium oxide coatings applied to niobium have an atomically sharp interface that has a lower fracture energy compared to Nb/Al₂O₃, resulting in improved interfacial debonding and composite fracture toughness.     

Quantifying Tstress controlled constraint by the master curve transition temperature T0

Specimen size, crack depth and loading conditions may effect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the master curve standard ASTM E1921-97, which is based on technology developed at VTT Manufacturing Technology. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases, this may lead to unnecessary repairs or even to an early “retirement” of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J small scale yielding correction, Q-parameter and the T_stress. Here, a relation between the T_stress and the master curve transition temperature T₀ is experimentally developed and verified. As a result, a new engineering tool to assess low constraint geometries with respect to brittle fracture has been obtained.     

Residual stress and constraint effects on cleavage fracture in the transition temperature regime

Defects in structural components are often associated with welds that may contain significant levels of residual stress. Whilst the primary load acting on the component may induce low constraint conditions at the crack tip, the presence of residual stresses, e.g. due to welding, can modify this constraint level and consequently influence the observed fracture toughness behaviour. This paper presents the results of a combined experimental and numerical programme aimed at exploring this issue. Cleavage fracture toughness data for high and low constraint specimens are presented with and without residual stresses. The results indicate that under certain conditions, the constraint-induced increase in cleavage fracture toughness may be eroded by the presence of a residual stress in the vicinity of the crack. The results are quantified with respect to two-parameter fracture mechanics in which the  T  and  Q  parameters are appropriately defined. Preliminary guidance is provided for the assessment of defects when residual stresses may influence crack-tip constraint.     

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 stresses on the strength and fracture energy of the brittle film: Multiple cracking analysis

The aim of this paper was to address the effect of the residual stresses within the brittle film on the substrate on the film strength, fracture energy, and interfacial shear strength (IFSS). Special analyses were performed on the SiO_x film/polyethulene terephthalate substrate systems. The residual stresses were evaluated by using the curvature method. The film strength, fracture energy, and IFSS were estimated on the basis of the multiple cracking analyses. In the multiple cracking analyses, the system was subjected to the combination of the residual stresses and the unidirectionally applied stress. Results showed that the relationship between the crack density in the film and the applied strain can be predicted by adopting the energy criterion on the basis of the knowledge on the residual stress distributions in the film segment. The film strength and fracture energy for the initiation of film cracking were almost proportional to the compressive residual stresses in the film. With increasing the compressive residual stresses within the film, the IFSS also increased.