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.     

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.     

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.     

Development of the Local Approach to Fracture over the Past 25 years: Theory and Applications

This review paper is devoted to the local approach to fracture (LAF) for the prediction of the fracture toughness of structural steels. The LAF has been considerably developed over the past two decades, not only to provide a better understanding of the fracture behaviour of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional linear elastic fracture mechanics and elastic–plastic fracture mechanics global approaches. The bases of this relatively newly developed methodology are first presented. Both ductile rupture and brittle cleavage fracture micromechanisms are considered. The ductile-to-brittle transition observed in ferritic steels is also briefly reviewed. Two types of LAF methods are presented: (i) those assuming that the material behaviour is not affected by damage (e.g. cleavage fracture), (ii) those using a coupling effect between damage and constitutive equations (e.g. ductile fracture). The micromechanisms of brittle and ductile fracture investigated in elementary volume elements are briefly presented. The emphasis is laid on cleavage fracture in ferritic steels. The role of second phase particles (carbides or inclusions) and grain boundaries is more thoroughly discussed. The distinction between nucleation and growth controlled fracture is made. Recent developments in the theory of cleavage fracture incorporating both the effect of stress state and that of plastic strain are presented. These theoretical results are applied to the crack tip situation to predict the fracture toughness. It is shown that the ductile-to-brittle transition curve can reasonably be well predicted using the LAF approach. Additional applications of the LAF approach methods are also shown, including: (i) the effect of loading rate and prestressing; (ii) the influence of residual stresses in welds; (iii) the mismatch effects in welds; (iv) the warm-prestressing effect. An attempt is also made to delineate research areas where large improvements should be made for a better understanding of the failure behaviour of structural materials.     

Using local out-of-plane compression (LOPC) to study the effects of residual stress on apparent fracture toughness

To study and understand the effects of residual stresses on fracture behaviour, it is necessary to introduce well characterised and reproducible residual stresses into laboratory fracture specimens. One technique capable of providing such residual stresses is local compression, where the local compression is applied to the sides of a test specimen. In this paper, the technique is used to create a residual stress field in compact tension, C(T), specimens. The specimens are used subsequently to study the effects of residual stress on fracture. Finite element studies show that significant changes to the distribution of the residual stresses occur when the position of the compression tools is changed relative to the crack tip. It is also revealed that both a single and double pair of compression tools can generate both tensile and compressive residual stresses in the vicinity of the crack tip depending upon the location of the tools relative to the crack tip. The impact of local compression is illustrated by experimental results from room temperature fracture tests performed on two aluminium alloys, Al2650 and Al2024. Tensile residual stresses, created by the application of a single pair of compression tools, reduced the initiation fracture toughness of Al2650 by about one half. The ductile tearing resistance of Al2024 decreases when a double pair of tools introduces tensile residual stresses. Conversely, the tearing resistance increases when compressive residual stresses are created through local compression.     

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.     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

BT20钛合金激光焊接接头的断裂韧性研究

对BT20钛合金及其激光焊接接头的断裂韧性进行了研究.同时分析了合金及激光焊接接头的硬度分布及显微组织.断裂实验表明,除了一个焊接接头紧凑拉伸(CT)试样是脆性启裂外,其它CT试样均在裂纹延性启裂并缓慢扩展后,发生脆性失稳断裂.母材的断裂韧性明显高于焊接接头,轧制方向对母材断裂韧性的影响不明显.焊接热影响区的断裂韧性介于母材和焊缝金属之间.本研究采用的焊后热处理没有改善焊接接头的断裂韧性,还有进一步恶化的趋势.添加活性剂对焊缝金属的断裂韧性没有明显作用,但对延性裂纹扩展长度有所改善.     

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.     

FATIGUE CRACK GROWTH LAWS FOR BRITTLE AND DUCTILE MATERIALS INCLUDING THE EFFECTS OF STATIC MODES AND ELASTIC-PLASTIC DEFORMATION

A fatigue crack growth damage accumulation model is used to derive laws for the fatigue crack growth rates of brittle and ductile materials. The damage accumulated during cyclic loading is assumed to be proportional to the cyclic change in the plastic displacement in the crack tip yielded zone. The static mode contribution to the fatigue damage is assumed to be proportional to some power of the crack tip displacement. The laws are applicable in either the small or large scale yielding regimes provided that the stress ratio remains positive. Static modes are assumed to be controlled by the fracture toughness value in brittle materials, and by the gradient of the crack growth resistance curve in ductile materials. In the analysis of ductile materials it is assumed that the crack growth resistance of the material is not significantly altered by fatigue crack growth.
The growth rate equations are expressed in terms of the near field value of the J -integral, i.e. the value which would be calculated from assuming the material deformed in a non-linear elastic manner during the increasing load part of the fatigue cycle. Examples are given of the predictions of the growth law for ductile materials. It is predicted that after the initiation of stable tearing the crack growth rate, when expressed in terms of the cyclic change in the stress intensity factor, depends on both the structural geometry and the degree of crack tip plastic deformation. In both brittle and ductile materials the fatigue crack growth rate is predicted to accelerate as the failure criteria relevant to static crack instability are approached.     

Finite element analysis and experimental evaluation of ductile-brittle transition in compact tension specimen

Using finite element analysis, metallographic observations and statistical analysis, the stress field ahead of stationary and growing cracks and the ductile-brittle transition mechanism in compact tension (CT) specimens have been evaluated. Compared to a stationary crack, a growing crack elevates the opening stress on the remaining ligament and this may be partially attributed to the re-sharpening of the crack tip after ductile growth. The area of material covered by the high opening stress of the same magnitude also increases with ductile crack growth. In this study, no significant difference for measured cleavage stress can be found for the specimens fractured with and without ductile crack growth. There is a large scatter for the distance between the cleavage initiation site and the stationary or growing crack tip. Cleavage fracture after some amount of ductile crack growth is attributed to the increase of both the opening stress and the area of material under high opening stresses. Finally, the lower bound toughness is predicted using a small data set statistical model in connection with constraint correction. The predicted values give the same trend as the lower bound of the experimental measurements from the lower-shelf to the temperature at which ductile crack growth occurs. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temperature Dependence of Brittle Fracture Toughness of Reactor Pressure-Vessel Steels upon Ductile Crack Growth

The main mechanisms of brittle fracture upon ductile crack growth are studied on the basis of the probabilistic model of brittle fracture and the deterministic model of ductile fracture, which were put forward by the authors earlier. The investigations are carried out on the reactor pressure-vessel steel 15Kh2NMFAA in the initial and embrittled states. The dependences of brittle-fracture probability on the stress intensity factor and the value of ductile crack growth are calculated for various temperatures. The temperature dependence of brittle fracture toughness in the initial and embrittled states is predicted with and without regard for ductile crack growth. The authors analyze the main factors that govern the above-mentioned relationships. The calculated results are compared to test data for CT-type compact specimens.     

The effect of welding residual stress on brittle fracture of plates with surface cracks

Two types of butt-welded wide plates (steel OX 522D) containing half-elliptical surface cracks (30 mm thick plates with the crack perpendicular to the weld and 100 mm thick plates with the crack parallel to the weld) were tested in the as-welded and thermally stress relieved conditions. The effects of welding residual stress and stress relief on brittle fracture were investigated. It was found that the influence of welding residual stress on surface crack fracture may be substantial, depending on the stress field and the crack orientation and geometry. The influence was found to be predictable with linear elastic fracture mechanics. Post weld heat treatment was found to remove most of the residual stresses and therefore reduce the fracture risk, provided the material toughness is not impaired.     

Thermal residual stresses in particulate composites and its toughening effect

In this paper, an accurate formula for calculating the thermal residual stress field in a particle-reinforced composite are presented. Numerical examples are given to show r-variations of the thermal residual stresses. The increase in fracture toughness of matrix predicted by the thermal residual stress field is compared well with the experimentally measured increase. This work was supported by the National Natural Science Foundation of China (No.50172053).     

On Influence of Non-Singular Stress States on Brittle Fracture

In the case of sufficiently brittle material the use of stress intensity factor as a fracture parameter alone is well justified within the Linear-Elastic Fracture Mechanics. This is because the singular stress field associated with the stress intensity factor is dominant near the crack tip. However, there are numerous experimental evidences that the critical stress intensity factor to cause fracture initiation (or fracture toughness) can be affected by the specimen geometry as well as loading conditions. To address this issue a number of twoparameter criteria have been proposed in the past, which often utilise non-singular terms of the classical asymptotic expansion of the stress field near the crack tip. Therefore, there is a problem of the selection of an appropriate parameter in addition to the stress intensity factor, which could account for various effects induced by the specimen geometry and loading on initiation of brittle fracture. This short paper demonstrates that brittle fracture conditions can be successfully predicted with various two-parameter criteria, and there are no clear advantages in the use of T-stress as the additional parameter in fracture criterion, in comparison with the next non-singular term, A ₁, of the asymptotic expansion.     

Dynamic fracture mechanics—A scientific tool for the prevention of catastrophic failure

The major area of research in dynamic fracture has been the extension of the concept of static fracture toughness to predict crack arrest for a propagating crack. In this work crack propagation due to a ductile (microvoid) mechanism and cleavage (brittle) mechanism, as well as transition from one mode to another, has been analysed theoretically. Dynamic fracture toughness as a function of crack velocity has been determined. Temperature distribution near a propagating crack tip has been predicted for plane stress condition. The effect of reflected stress wave in a single edge notch specimen under transient crack growth conditions has also been analysed.     

Effects of crack depth on elastic-plastic fracture toughness

Short crack test specimens (a/W 0.50) are frequently employed when conventional deep crack specimens are either inappropriate or impossible to obtain, for example, in testing of particular microstructures in weldments and in-service structures containing shallow surface flaws. Values of elastic-plastic fracture toughness, here characterized by the crack tip opening displacement (CTOD), are presented for square (cross-section) three-point bend specimens with a/W ratios of 0.15 and 0.50 throughout the lower-shelf and lower-transition regions. Three dimensional, finite-element analyses are employed to correlate the measured load and crack mouth opening displacement (CMOD) values to the corresponding CTOD values, thus eliminating a major source of experimental difficulty in previous studies of shallow crack specimens. In the lower-transition region, where extensive plasticity (but no ductile crack growth) precedes brittle fracture, critical CTOD values for short crack specimens are significantly larger (factor of 2–3) than the CTOD values for deep crack specimens at identical temperatures. Short crack specimens are shown to exhibit increased toughness at the initiation of ductile tearing and decreased brittle-to-ductile transition temperatures. Numerical analyses for the two a/W ratios reveal large differences in stress fields ahead of the crack tip at identical CTOD levels which verify the experimentally observed differences in critical CTOD values. Correlations of the predicted stresses with measured critical CTOD values demonstrate the limitations of single-parameter fracture mechanics (as currently developed) to characterize the response.     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ _F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.     

Crack propagation in ceramics under cyclic loads

Stable crack growth is observed in notched plates of polycrystalline alumina subject to fully compressive far-field cyclic loads at room temperature in a moist air environment andin vacuo. The fatigue cracks propagate at a progressively decreasing velocity along the plane of the notch and in a direction macroscopically normal to the compression axis. The principal failure events leading to this effect are analysed in terms of notch-tip damage under the far-field compressive stress, microcracking, frictional sliding and opening of microcracks, and crack closure. An important contribution to such Mode I crack growth arises from the residualtensile stresses induced locally at the notch-tip when the deformation within the notch-tip process zone leaves permanent strains upon unloading from the maximum nominal compressive stress. It is shown that the phenomenon of crack growth under cyclic compressive stresses exhibits a macroscopically similar behaviour in a wide range of materials spanning the very ductile metals to extremely brittle solids, although the micromechanics of this effect are very different among the various classes of materials. The mechanisms of fatigue in ceramics are compared and contrasted with the more familiar examples of crack propagation under far-field cyclic compression in metallic systems and the implications for fracture in ceramic-metal composites and transformation toughened ceramic composites are highlighted. Strategies for some important applications of this phenomenon are recommended for the study of fracture mechanisms and for the measurement of fracture toughness in brittle solids.