Bilinear CTOD/CTOA scheme for characterisation of large range mode I and mixed mode stable crack growth through AISI 4340 steel

An investigation has been reported concerning characterisation of large span stable crack growth (SCG) through AISI 4340 steel in terms of CTOD/CTOA under both mode I and mixed (I and II) mode loadings. The characterisation has been possible through finite element analysis of published experimental results with compact tension type of specimens. As against the earlier observations by many investigators of a bilinear CTOD/CTOA variation, decreasing initially and constant later, characterising the crack growth through other materials, an increasing initially and constant later type of variation is found to be suitable for AISI 4340 steel. The same variation is found to characterise both mode I and mixed mode SCG. The starting value of CTOD/CTOA is 0.035 mm/0.0875 rad; the value at the later stages is 0.08 mm/0.20 rad. The same variation is found to predict accurate enough for engineering applications the initiation (P_i) and maximum (P_max) loads and the variation of load-displacement diagrams over a span of crack growth up to 10 mm.     

A scheme for finite element analysis of mode I and mixed mode stable crack growth and a case study with AISI 4340 steel

A new scheme for elastic–plastic finite element analysis has been proposed for the study of stable crack growth (SCG) from initiation to instability in both mode I and mixed modes (I and II). The scheme is based on node-release technique and helps to determine the variation of fracture load with crack extension without requiring much computer storage and time. The scheme permits predictions of load variation with load line displacement (LLD), maximum fracture load, crack tip current plastic zone and crack edge profile. In the analysis the condition for crack extension at every stage of the SCG is considered to be governed by CTOA/COD reaching a critical value. The scheme of analysis is different from the ones proposed by earlier investigators. The whole SCG is analysed in a few stages using the ANSYS software and a single discretization. Element arrangement in the discretization is decided from the very beginning; it has a capability of accommodating changes in boundary conditions arising out of crack extension in the later stages. Each stage is analysed afresh ignoring state of stress–strain reached at a material point at the end of the previous stage. Case studies on both mode I and mixed mode presented considering AISI 4340 steel, which is widely used in nuclear power industry, indicate that the SCG through it can be characterized in terms of a single COD or CTOA. Predictions for the initiation and maximum fracture loads in both the cases compare very closely with the experimental data reported. The results presented also include the value of critical COD/CTOA (0.035 mm/0.0875 rad) characterizing the SCG through the steel and show that the initiation load is not significantly affected by crack tip radius up to 0.05 mm.     

Experimental investigation on ductile stable crack growth emanating from wire-cut notch in AISI 4340 steel

An experimental investigation on the stable crack growth (SCG) behaviour in AISI 4340 using CT type specimen with a sharp slit (0.05 mm) under mode I and mixed modes (I and II) loading is presented. The slit was made in the specimen through wire cutting technique. Different combinations of loading angle and ratio of original crack length to specimen width (a₀/W) are examined. Data concerned with direction of initial crack extension, load–load line displacement (L–LLD) diagrams, initiation and maximum loads, range of stable crack growth, crack tip blunting, crack front geometry, fracture surfaces and their scanning electron micrographs are obtained. A noticeable blunting effect is observed prior to crack initiation. Although the crack initiates from a straight front, a considerable front tunnelling effect occurs as the crack extends. Under mixed mode, the crack extension takes place initially almost along a straight path, inclined with the main crack. The loading angle and initial crack length affect the initiation (P_i) and maximum (P_max) loads significantly, but the ratio between P_max and P_i remains almost constant. The direction of initial stable crack extension due to mixed mode loading is determined throughout an elastic finite element analysis. There is a good agreement between the experimental and predicted results.     

Large stable crack growth in fracture mechanics specimens

According to the J concept, information is reported about the crack resistance behaviour up to 8 mm crack growth of side-grooved CT-25 as well as CCT-25 specimens made from German standard steel StE 460. Numerical simulations controlled by J_R curves make the calculation of J from the stresses and strains of specimen models during large crack growth feasible. These data allow a comparison to standards and rules describing the evaluation of J from experiments. Using stress, strain and displacement fields from a plane-strain finite-element analysis, the extended J concept is discussed concerning larger ductile crack growth. Additionally, the distribution of other fracture mechanics parameters such as the crack tip opening displacement (CTOD) and the crack tip opening angle (CTOA) are presented for larger crack growth.     

Evaluation of SCC crack behavior in zirconium and zircaloy-2 using nonlinear fracture mechanics parameters

Applicability of nonlinear fracture mechanics parameters, i.e. J-integral, crack tip opening displacement (CTOD), and crack tip opening angle (CTOA), to evaluation of stress corrosion crack (SCC) propagation rate was investigated using fully annealed zirconium plates and Zircaloy-2 tubing, both of which produce SCC with comparatively large plastic strain in an iodine environment at high temperatures.Tensile SCC tests were carried out at 300°C for center-notched zirconium plates and internal gas pressurization SCC tests at 350°C, for Zircaloy-2 tubing, to measure the SCC crack propagation rate. The J-integral around semi-elliptical SCC cracks produced in Zircaloy-2 tubing was calculated by a three-dimensional finite element method (FEM) code.The test results revealed that the SCC crack propagation rate dc/dt could be expressed as a function of the J-integral, which is the most frequently used parameter in nonlinear fracture mechanics, by the equation dc/dt = C · Jⁿ, where C and n were experimental constants.Among the other parameters, CTOD and CTOA, the latter appeared to be useful for assessing the crack propagation rate, because it had a tendency to hold a constant value at various crack depths.     

包含过热区的焊接接头强度组配对CTOD的影响

利用试验研究和数值分析方法，对模拟焊接接头三点弯曲试样不同强度组配对裂纹尖端张开位移（CTOD）的影响进行了研究，本研究的模拟焊接接头试样是通过电子束焊接法焊制的，数值分析中采用了三金属模型，较以往的二金属模型更接近于实际，结果表明，不同的焊接接头强度组配对CTOD有不同程度的影响；无量纲载荷P／PY和CTOD裂纹扩展驱动力关系曲线与极限载荷的选取有很大关系，二维数值计算与试验结果在无量纲载荷P／PY较小时具有良好的一致性，但随P／PY的增加，二者的偏差增大。     

Modified crack closure integral based computation of stress intensity factors for 2-D thermoelastic problems through boundary element method

A modified crack closure integral (MCCI) based computation of stress intensity factors (SIFs) for thermal loading through boundary element method (BEM) is presented. Simple relations are given for the determination of stress intensity factors (SIFs) using the BEM results for linear, quadratic and quarter point elements employed around the crack tip. Examples of crack under mode I, mode II and mixed mode thermal and/or mechanical loading are examined. The computed SIFs are compared wherever possible with solutions available in the literature. The agreement is good. The effect of crack tip element size on the accuracy of results is reported.     

Time dependent ductile crack extension in A533B class I steel

Four wide plate specimens manufactured in A533B Class I, 90 mm thick by 500 mm wide containing through-thickness or semi-elliptical surface fatigue cracks were tested at +70°C. These specimens were subjected to a series of increasing applied loads, each of 100 h duration, until failure. Testing was performed using a computer interactive 40 MN load controlled tensile testing rig. Values of the fracture toughness parameters J and crack tip opening displacement (CTOD) were derived from the recorded values of applied load, plate extension and crack mouth opening displacement.The influence of loading rate, degree of yield containment and crack orientation on the time dependent behaviour is assessed and compared with data obtained from wide plate and bend tests under monotonic loading and from bend tests conducted with a variable loading rate, with hold periods, under crack mouth opening control. Interpretation of the results provides a clearer understanding of low temperature time dependent ductile crack extension and enables the identification of the conditions under which this phenomenon is apparent, to allow the necessary adjustments to failure assessments.     

In situ crack growth observation and fracture toughness measurement of hydrogen charged Zircaloy-4

The effect of hydrogen on the fracture behaviour of a Zircaloy-4 alloy was analysed performing simultaneous fracture mechanics tests of small SE(B) specimens and in situ observation of crack initiation and propagation inside the chamber of a scanning electron microscope. Load and displacement were continuously measured and J_IC, J-R curves and CTOD determinations were obtained. Detailed images of the zone close to the crack tip were taken and the resistance to crack growth was correlated with hydrogen content and hydride morphology. The size and orientation of hydride precipitates showed an important influence on the fracture process. A good agreement with results obtained using standard CT specimens was met.     

Liquid metal embrittlement of T91 and 316L steels by heavy liquid metals: A fracture mechanics assessment

LME of the martensitic T91 and the austenitic 316L steels have been investigated in the CCT geometry in the plane-stress condition. Using such a geometry, premature cracking induced by a liquid metal (PbBi and Hg) can be studied using a fracture mechanics approach based on CTOD, J-Δa and fracture assessment diagram. One is able to measure a reduction of the crack tip blunting and a reduction of the energy required for crack propagation induced by the liquid metal. In spite of some limitations, this qualitative evaluation shows that liquid metals do not induce strong embrittlement on steels in plane-stress condition. Rather, the effect of the liquid metal seems to promote a fracture mode by plastic collapse linked with strain localization. It indicates that the materials, in spite of a potential embrittlement, should still be acceptable in terms of safety criteria.     

Analysis of stable crack growth across welded fusion line: Japanese round-robin

Bimaterial CT specimens are numerically analyzed in the elastic-plastic states. By changing the material constants and the distance between the crack tip and the phase boundary, the parametric analyses are conducted. J integral evaluated by the line integration is compared with that obtained by the empirical formula by Merkel-Corten. The effects of the inhomogeneities on the accuracy of the J integral evaluation are discussed. Next the stable crack growth analyses are conducted. Using the relation between a and load-load line displacement obtained experimentally, the generation phase analyses are carried out. J integral, T^* integral and CTOA are evaluated and the effects of the fusion line are discussed.     

Ductile crack growth simulation from near crack tip dissipated energy

A method to calculate ductile tearing in both small scale fracture mechanics specimens and cracked components is presented. This method is based on an estimation of the dissipated energy calculated near the crack tip. Firstly, the method is presented. It is shown that a characteristic parameter G_fr can be obtained, relevant to the dissipated energy in the fracture process. The application of the method to the calculation of side grooved crack tip (CT) specimens of different sizes is examined. The value of G_fr is identified by comparing the calculated and experimental load line displacement versus crack extension curve for the smallest CT specimen. With this identified value, it is possible to calculate the global behaviour of the largest specimen. The method is then applied to the calculation of a pipe containing a through-wall thickness crack subjected to a bending moment. This pipe is made of the same material as the CT specimens. It is shown that it is possible to simulate the global behaviour of the structure including the prediction of up to 90-mm crack extension. Local terms such as the equivalent stress or the crack tip opening angle are found to be constant during the crack extension process. This supports the view that G_fr controls the fields in the vicinity near the crack tip.     

Fracture mechanics behavior of the T91 martensitic steel in contact with liquid lead-bismuth eutectic for application in an accelerator driven system

The fracture toughness of the T91 martensitic steel in liquid lead-bismuth eutectic has been measured at 300 °C in plane stress and plane strain conditions. The effect of achieving wetting at the crack tip prior starting mechanical testing is demonstrated to be the key factor for a correct evaluation of the potential effect of LBE on fracture toughness. In plane stress, one observes a serrated fracture mode associated with a reduction of fracture toughness between 20% and 30%. The toughness reduction is higher in plane strain where the cleavage fracture mode prevails. The difference between the two fracture modes is due to the higher plastic deformation level reached at final fracture in plane stress and to the higher crack growth rate in plane strain. These results will be useful for the design of future nuclear systems cooled by LBE planning to use martensitic steels as structural materials.     

Fracture mechanics in creep situation interpretation of results on a test specimen

Fracture mechanics in creep situation is a difficult challenge for the 1990s. In France, CEA Saclay has conducted experimental tests on compact tension (CT) specimens at 650°C in order to investigate crack initiation under creep situations. The constitutive material is the 316SPH austenitic stainless steel used for most LMFR structures.Numerical simulations using SYSTUS code and simplified method analysis were performed on one of the tests (CT specimen at 650°C under constant load) to compare some parameters (notch opening, initiation time) with experimental values. The material constitutive law was represented by the complete elasto-viscoplastic CHABOCHE model for computation. Owing to geometrical characteristics such as thickness, the situation of the CT specimen was likely to be intermediate between plane stress and plane strain assumptions. From C^* parameter, incubation time obtained using the R5 rule was conservative in comparison with the test result.The continuum damage model developed at Ecole des Mines de Paris has also been used to assess creep damage in the notch tip area. The crack initiation time has been deduced from critical damage at characteristic distance (X_c = 0.05 mm). Considering critical damage specifically, for a CT specimen (D_c = 0.05), initiation time obtained was higher than the test result.The results of this study will contribute to the development of a methodology for nocivity analysis of cracks in creep situation.     

Damage, crack growth and fracture characteristics of nuclear grade graphite using the Double Torsion technique

The crack initiation and propagation characteristics of two medium grained polygranular graphites, nuclear block graphite (NBG10) and Gilsocarbon (GCMB grade) graphite, have been studied using the Double Torsion (DT) technique. The DT technique allows stable crack propagation and easy crack tip observation of such brittle materials. The linear elastic fracture mechanics (LEFM) methodology of the DT technique was adapted for elastic-plastic fracture mechanics (EPFM) in conjunction with a methodology for directly calculating the J-integral from in-plane displacement fields (JMAN) to account for the non-linearity of graphite deformation. The full field surface displacement measurement techniques of electronic speckle pattern interferometry (ESPI) and digital image correlation (DIC) were used to observe and measure crack initiation and propagation.Significant micro-cracking in the fracture process zone (FPZ) was observed as well as crack bridging in the wake of the crack tip. The R-curve behaviour was measured to determine the critical J-integral for crack propagation in both materials. Micro-cracks tended to nucleate at pores, causing deflection of the crack path. Rising R-curve behaviour was observed, which is attributed to the formation of the FPZ, while crack bridging and distributed micro-cracks are responsible for the increase in fracture resistance. Each contributes around 50% of the irreversible energy dissipation in both graphites.     

金属材料裂纹冲击韧性评定方法研究

工程结构在复杂环境下长期服役后,裂纹的萌生和发展难以避免。对于需要承受爆炸与冲击的工程结构,需要对所用材料的裂纹冲击韧性进行评定,避免裂纹出现可能导致的冲击脆性断裂。基于Instron VHS高速材料试验机,开发了一套材料动态断裂试验装置,测量了4种具有高冲击功金属材料的裂纹冲击韧脆转变过程,并研究了影响金属材料裂纹冲击韧脆转变速率的因素。发现材料夏比冲击功并不能完全反应裂纹的冲击韧性,预制裂纹与否、试样约束方式和试样裂尖约束因子都会影响金属材料裂纹冲击试验中的韧脆转变速率。基于以上研究结果,提出了金属材料裂纹冲击韧性评定方法的基本思路。      

Strain distribution around a crack tip in high temperature environment using picture processing

A new optical strain measuring method developed by the authors is described. Here, we employ a simple method which uses point recognition picture processing and the least square approximation method.The surface of the specimen for which we are going to obtain the strain distribution is marked with points using a punch or a paint marker beforehand. At each loading stage, the digital data of the black and white picture of the specimen's marked surface are taken with the television camera under the control of the computer to which the data are sent. From these data, the locations of the marked points at each loading stage are obtained by the picture processing technique. Using these locations decided, we obtain the least square approximation of the displacement distribution, and then the strain distribution.To show the effectiveness of the present technique, the method is applied to the strain measurement near the crack tip in the CT specimen of Type 304 stainless steel. Because of the high ductility of this material, the crack tip blunting is notable so that the crack tip opening displacement observed by this method is as large as 2.5 mm at the specimen surface before initiation.Next, the strain distributions of a center-notched panel made of Type 304 stainless steel under high temperature creep condition are obtained.It is found from the above two experiments that the present strain measuring technique is powerful for the measurement of high strain, say more than 1%, whereas it is unsuitable to apply to the case of small strain at the present developing stage.     

Short fatigue crack propagation and effect of notch plastic field

In engineering application, almost all structures and components contain notches or holes. They often experience severe fatigue loading, and have been recognized as a potential site for small fatigue crack initiation and propagation. In this paper, the effects of notch plastic field on small fatigue crack initiation and propagation from notch member, under cyclic tensile loading control, are investigated. Experiment shows that small crack initiates from notch specimen at far higher rate than that of smooth specimen; small crack propagation is still faster than that of smooth specimen within notch plastic field, though this difference is progressively lessening; beyond notch plastic zone, small crack growth rate is approaching long crack growth rate. Analysis via finite element and analytical method reveals that notch plasticity has key influence on small crack initiation, crack tip generated plasticity has critical impact on small crack propagation within notch plastic field, while plasticity induced crack closure has dominant effect on crack propagation out of notch plastic field. A comparison between experimental and analytical results is made to identify the mechanisms of small fatigue crack initiation and propagation within notch plastic field.     

Fracture criterion of a mixed-mode crack based on CED (Crack Energy Density)

The CED (Crack Energy Density) in an arbitrary direction, , is defined as the quantity which has the meaning of strain energy area density in the plane containing a crack front line without any restriction on constitutive equation. We may expect that, as far as the opening type fracture occurs, a mixed mode crack begins to grow in the direction where (mode I contribution of ) takes the maximum value, , when reaches a critical value peculiar to a material (we call this criterion criterion). In this paper, the applicability of this criterion to elastic-plastic fractures is studied based on the fracture experiments on specimens of Aluminum alloy with a crack inclined to the loading axis and it is demonstrated that the onset and the direction of crack growth can be estimated by criterion in either case of fractures with relatively small yielding region and those with large yielding region. The applicability of criterion to elastic (quasi-elastic) fractures is also shown through the comparison of the result by criterion with the results by other criteria and experimental results.     

Relationship between ductile crack initiation and void volume fraction

An investigation on ductile crack initiation in structural steel has been made, based on the concept of Gurson's yield function for porous material. First, the condition of ductile crack initiation in the uniform stress field has been investigated. The condition of ductile crack initiation under various stress triaxiality obtained from the tests on axisymmetric notched tensile specimens is well expressed by the condition of constant void volume fraction analytically obtained from Gurson's model. This result means that the condition of constant void volume fraction may be used as the criterion of ductile crack initiation. Secondly, the behavior of void growth and ductile crack initiation in the area near the notch tip under mode I and mode II loading has been investigated. Under mode I loading, the increase in void volume fraction around the notch with an increase in applied load agrees well with the behavior of porous material predicted by the finite element analysis based on Gurson's yield function, and the ductile crack initiation can be predicted by the concept of critical void volume fraction as in the case of uniform stress-strain field given above. The same criterion is not applicable to the crack initiation under mode II loading and further study is needed.