The three dimensional J-integral expressions were introduced and evaluated by using finite element method. The thick plate with a through crack and the compact type specimens were elastically analyzed, and the distributions of the JX values along the crack front were obtained. By changing the thickness of the specimen, the thickness effects were studied. It was shown that the second term of the three dimensional J-integral expression was the main factor for the thickness effect. The CT specimens with several depths of side groove were also analyzed. For a quarter inch thickness specimen, it was shown that 10% side groove gave the equal J values along the crack front.
JIc tests were carried out on two steels and one aluminum alloy by means of the ASTM and JSME R-curve methods as well as the JSME streched-zone-width (SZW) method. The SZW method tended to overestimate the JIc values at initiation of ductile tearing. The ASTM method, which also had a tendency to overestimate these JIc values, seemed to be the most convenient and stable procedure among the three methods. The JSME R-curve method gave the smallest JIc values which were physically closest to the crack initiation.
Fracture toughness tests were performed in the transition region on ASTM A508 Cl.3 and A470 Cl.6 steels using about 300 specimens of 0.5T, 1T, 2T and 4T compact tension (CT) specimens. The KJ values which are converted from Jc of the smaller specimens indicated a wide scatter ranging from below the KIc value to much higher toughness. The fracture behavior was investigated by a scanning electron microscope in detail and the sources of scatter of the toughness in small specimens were studied. The fast brittle fracture behavior in the transition region can be deviled into two regions: (1) the region where fracture occurs on a blunting line (Region I) and (2) the region where fracture occurs on an R-curve (Region II). The scatter of the KJ values is caused by the amount of crack extension contained in the specimens. The methods to obtain the fracture toughness equivalent to the KIc per ASTM Method from the KJ value were presented. In Region II a modified R-curve method is proposed. In Region I the lowest bound of KJ values obtained using specimens of which number meets the requirement of NB≥3000Jc/σY is recommendable, and this method may also be used in Region II.
The total volume fraction of second phase particles, fv, has been well related to the plane-strain fracture toughness, KIc, of the material. From this point of view, the influence of the distance from a pre-crack tip to an inclusion on both the stable crack initiation mechanism and the critical stretched zone width, SZWc, as a measure of localized fracture toughness along the crack front, was investigated utilizing electron fractography. The materials used were five aluminum alloys, 5083-O, 2017-T3, 2024-T3, 7075-T6, and 7N01-T6. The results obtained are summarized as follows: (1) For the aluminum alloys used, the following relationships between the sub-critical stretched zone width, SZW and J-integral do not stand; SZW=C1J/E (1) SZW=J/C2σfs (2) where E is Young's modulus and σfs is flow stress. However, for the intermediate strength aluminum alloys (2017, 2024, 7N01), both equations can stand apparently. (2) According to the fractographic observation, there exist three types of stable crack initiation mechanisms. (3) The variation of localized fracture toughness, SZWc, along the crack front arises due to the variation of the distance from the pre-crack tip to the inclusion, which causes the change of stable crack initiation mechanisms.
One of the most serious accidents which might possibly occur in piping systems is the sudden severing of pipe by tearing instability. Among safety assessment methods against this kind of fracture, the tearing instability theory based on the J-integral resistance curve is believed to be the most attractive one, because it can take account of compliance which is one of the important factors for tearing instability. This paper firstly presents tearing instability experiments using center and double-edge notched specimens. Load was applied to the specimens through a pipe tab with high compliance. Tearing instability occurred in all specimens after maximum load. The instability was predicted to take place when the value of Tappl, which is related to specimen configuration, compliance and other parameters, exceeded that of Tmat, which is concerned with the slope of J-integral resistance curve. The predicted instability point for each test compared well with the experimental point. Next, the paper proposed a formula of calculating the value of Tappl for a circumferential crack which lies in piping systems. The formula had been limitted to the simplest configuration of piping system, i.e. a straight pipe subjected to bending moment at both ends, because actual piping systems have three-dimensional structures, and that made it difficult to obtain the formula which took account of the overall compliance quantitatively. The paper showed that the problem for actual three-dimensional piping systems could be reduced to the equivalent problem of a straight pipe subjected to bending, where the equivalent length of straight pipe could be calculated from conventional finite element analysis of the piping system. The proposed formula can be used for the safety assessment of piping systems against tearing instability.
The effects of specimen geometry on the initiation and growth of ductile fracture from fatigue precrack have been investigated. Tests were made on the center-notched specimens with 5mm side ligament (specimen-CN5) and the side-notched specimens with the ratios of the ligament to notch depth, 5mm/22.5mm, 10mm/20mm, and 20mm/15mm (specimen-SN5, -SN10, and -SN20, respectively). Of these specimens, the stress triaxiality was largest in Specimen SN5 and smallest in CN5. 3 point bend specimens and CT specimens were also used as the standard specimens. Specimen-CN5 has shown the largest δi and Specimen-SN5 the smallest δi and Ji, whereas δi's and Ji's of other specimens have shown about the same values, where δi and Ji are COD and J at ductile crack initiation, respectively. Though the effect of specimen geometry on the ductile crack “initiation”was obvious in the above results, the effect on ductile crack“growth”was not clear in the present tests. The result that COD at the crack tip decreased from δi to δp as the crack grew from the precrack tip was explained by considering the effect of plastic strain-stress triaxiality history at each point of fracture until ductile fracture occurred at that point.
The processes of nucleation and growth of voids and formation of ductile cracks in tensile tests were investigated on plain and notched specimens of 7:3 brass. The main results obtained are as follows. (1) Voids appeared at nearly the ultimate tensile stress. The locations of void formations were grain boundaries or the inside of grain. (2) A crack was produced by the coalesence of the secondary micro-voids appearing in the highly deformed region (slip band) emanating from the initial void. The propagation of the crack proceeded by the similar process. (3) In cup and cone fracture, the mechanisms of fracture in cup- and cone-parts were nearly the same.
This paper presents theoretical considerations on the expressions for the dynamic energy release rate in elastic crack propagation. The validity of the expressions, which have been proposed by Erdogan, by Achenbach and by Freund, is discussed on the basis of the fundamental expression defined by an overall energy rate balance. The energy release rate is divided into the usual quasi-static energy release rate plus a non-positive dynamic contribution; they are discussed as the strain energy release rate for the former and as the kinetic energy generating rate for the latter. They will be useful as new parameters related to the dynamical behavior of crack propagation. The mathematical derivations given here are not in detail, but rather the background of the assumptions and physical considerations of the results are emphasized.
The X-ray fractography was applied to the compact and ESSO specimens of pressure vessel steels for nuclear reactors to evaluate the dynamic fracture toughness KID during brittle crack propagation. The relation between KID and the crack velocity was studied. In the compact specimen, KID decreased as the crack propagated and its value at crack arrest was equal to KIa but smaller than KIm. The steady crack velocity in the compact specimen at-60°C was about 550m/sec, at which KID was almost equal to KIm. The relation between the steady crack velocity and the arrested crack length was similar to the experimental and analytical results obtained previously on DCB specimens. The dynamic fracture toughness during the crack propagation became greater with an increase in both crack velocity and temperature, while it was independent of the test method.
This paper deals with the fracture phenomenon of a cracked beam of ductile material under dynamic electromagnetic force. The fracture analysis was carried out by using the dynamic finite elements with the special singularity. Then, the present analysis was applied to determine the dynamic fracture toughness of the material.
The dynamic fracture toughness values of glass mat reinforced polyester laminates were compared with the analytical values of dynamic stress intensity factor, and their temperature dependence was discussed using instrumented Charpy test results. The results obtained are as follows: (1) The ratio of dynamic fracture toughness KId to the static one KIS, which was obtained by the finite element method, decreased with time by oscillating around one, when the load increased at a constant rate. The ratio of KId/KIS was between 0.99 and 1.1, when the loading speed was about 0.55kgf/μs and KIS was greater than 30kgf/mm3/2 for EW test specimens, and when the speed was about 0.35kgf/μs and KIS was greater than 20kgf/mm3/2 for FW test specimens. The difference between the dynamic fracture toughness values obtained by the static K-calibration using the maximum load and by the dynamic K-calibration was smaller than the variation of measured values. (2) The dynamic fracture toughness values of EW specimens decreased slowly as the temperature became higher, while those of FW specimens were about constant at temperatures below 60°C. The toughness values of both specimens decreased rapidly as the temperature became higher than the thermal deformation temperature of resin (about 90°C). This temperature dependence of toughness was different from that of specific absorbed energy.
The relationship between the impact fatigue crack growth rate and the stress intensity factor range has been investigated by using the impact fatigue testing machines of several types. However, in evaluating the stress intensity factor the influence of the inertia effect has not yet been completely elucidated. The purpose of the present paper was to establish the mensuration of the dynamic stress intensity factor in the repeated impact three point bending test, and to investigate the effect of impact loading on fatigue crack growth rate. Contact force between the falling cylinder and the cracked beam was analyzed by applying the Hertz law and the compressive force in the cylinder was determined. The dynamic stress intensity factor was also determined by using the simple formula developed in the previous paper. Comparison of the analytical results with the experimental ones suggests that in the low impact velocity range, the dynamic stress intensity factor can be fairly well estimated by the static formula together with the output of the strain gauges which are glued on the cylinder. Impact fatigue tests were carried out on the specimens of annealed 0.46% carbon steel and aluminum alloy. The experimental results indicate that the influence of duration of impulsive loads is larger for carbon steel than for aluminum alloy.
Fatigue crack propagation tests were carried out on an aluminum alloy, ZK141-T7, under stationary varying loading conditions including random loading at relatively high stress intensity region and crack closure behaviors were investigated. It was found that the crack opening point under varying loadings was determined by the maximum range-pair of K and its R ratio and equal to that of the constant amplitude test of the same ΔK and R. Moreover, the estimation method of fatigue crack propagation rate based on the modified Miner's rule of crack propagation in terms of the effective stress intensity range-pair, which was proposed previously for the tests on steels, was confirmed to be applicable in this case, too.
In fatigue crack growth, crack tip blunting and resharpening occur within every cycle. Thus the first requisite for fatigue threshold may be considered as fulfilment of the condition of dislocation group emission from the crack tip. On the other hand, it has been experimentally observed that fatigue threshold stress intensity depends on the ferrite grain size. Therefore, the second requisite for fatigue threshold may be to satisfy the mechanical relation between the emitted dislocation group and the grain boundary. Thus, herein firstly the mathematical formula for fatigue threshold has been derived based on the first requisite mentioned above as the rate determining process. The criterion for fatigue threshold is proposed based on the condition of fulfilment of both the first and the second requisites. The model in this criterion is as follows. The fatigue threshold is considered as the stress intensity required to let the lead dislocation after emitted from the source reach the grain boundary. That is, when this condition is fulfiled, a micro crack initiates at the grain boundary by piled-up stress concentration, and, then, the main crack joins with this micro crack. Thus the fatigue crack growth will occur. Finally the criterion proposed is compared with the experimental results in literatures and also with other criteria, and the considerations were made.
Fatigue crack threshold values for 13Cr cast steel and 304 stainless steel were obtained in different environment, i. e., in room air, in hermetic sealed air which is quasi-inert environment and in water. Furthermore, the fatigue strength of 13Cr cast steel specimens with small shrinkage cavities was obtained in room air and in water. The threshold stress intensity value for a small defect was lower than that for a large crack, especially at a negative stress ratio. The threshold cyclic-plastic-zone-size criterion, which was proposed by the authors, could evaluate the fatigue threshold values for different stress ratios, by regarding defects as cracks. In water corrosion environment, the threshold value for a small defect could not be established and it was markedly lower than that for a large crack. The fatigue crack threshold values in room air were as high as twice of those in the quasi-inert environment. This was attributed to the wedging effect of metal oxide formed on crack surfaces. Water corrosion did not reduce the threshold value at a high stress ratio, while it reduced a lot of at a negative stress ratio. A model for oxide induced fatigue crack closure behavior was proposed, which explains the effects of the environment and stress ratio on the fatigue crack threshold values.
Fatigue tests were carried out on fatigue crack growth properties of small as well as large surface cracks in SUS 304 stainless steel at 538°C, by using plate specimens with surface notches of various shapes and small plate specimens with a small artificial pit. All the data of the fatigue crack growth rate obtained in the present tests were correlated with the stress intensity factor range ΔKI, so that the applicability of linear fracture mechanics to the fatigue crack growth of surface cracks at elevated temperature was investigated and discussed in comparison with the data of through cracks at elevated temperature and those at room temperature. It was found that the fatigue crack growth properties of surface cracks followed the same properties of through cracks even at 538°C and depended on test frequency in the same manner as through cracks. And it was observed that the fatigue crack growth properties of small surface cracks in plastic regime depended slightly on applied stress level. The data points, however, fell within a relatively narrow scatter band for a wide range of the applied stress levels and almost agreed with the data of through cracks. Therefore, under the present experimental conditions, linear fracture mechanics is to some extent applicable to the fatigue crack growth behavior of surface cracks at 538°C.
In the past, we have conducted the tests on the macroscopic through-crack propagation of ductile steels in creep, and found out the nonlinear fracture mechanical behavior. The investigation of fracture mechanics of microcrack growth is important to clarify the characteristics of creep fracture as well as to indicate a guide for the evaluation of cracks or flaws in high temperature structures. In this study, a continuous observation of intergranular microcrack growth at the surface of coarse grained smooth specimens of 316 stainless steel was made during creep tests at 650 and 800°C in vacuum. The initiation of surface cracks was detected at the early stage of steady state creep. Surface cracks increased in number, and some of them grew intermittently to the length of a few grain boundaries, while the crack opening displacements increased rather momentarily. The aspect ratio scattered from 0.6 to 1.5 for shallow cracks of one or two grain boundary length. It was found that the growth rate of every cracks at the surface had a roughly linear relation to the creep J-integral estimated on the basis of the steady creep rate and modified by crack shape correction factors, and that the relation corresponded with that of macroscopic through-crack propagation rate of the CCP specimens. A better correlation was obtained between the surface crack length and the cumulative creep J-integral estimated by the crack opening displacement.
The branching and growth mechanism of stress corrosion cracks in quenched-and-tempered SNCM 8 steel in 3.5% NaCl solution was analysed from a view point of fracture mechanics. The intermittent crack growth behavior was detected. The crack increment in each step of discontinuous crack growth was smaller than the plastic zone size and larger than the twice of the crack tip opening displacement. The crack branching mode was shown to be strongly dependent upon the tempering temperature. The effect of crack branching on crack growth kinetics was separately discussed based on a mechano-chemical model of stress corrosion cracks.
In order to determine the K-value of the complex cracked bodies within the accuracy of practical use, a new experimental method was proposed based on the brittle fracturing of epoxy resin. By comparing the experimentally determined K-value of a standard specimen with the calculated value, the accuracy of the proposed method was first checked. Then, the K-value determination tests of a specimen with cracks of different length in both sides of the specimen surface and a specimen having a semicircular part-through crack were carried out. Through the experiments, it is shown that the proposed method is practical and useful in determining the K-value of the cracked bodies.