Journal of the Society of Materials Science, Japan

FEM Analysis on the Neighbourhood of Crack Tip by Constitutive Equation of Voided Material

Hiroshi MIYAMOTO, Masanori KIKUCHI, Mitsuhiro KUBO, Tsuyoshi INOHIRA

1988 Volume 37 Issue 419 Pages 878-884
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.878

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Large deformation finite element analysis with modified Gurson's constitutive relation was applied to the I void and 2 voids models. Deformation, distribution of equivalent plastic strain and void volume fraction were obtained, and the condition of the localization of deformation given by Rudnicki and Rice was applied to study the possibility of the ductile fracture by the localization. Furthermore, the relation between the diameter of voids and J was compared with the experiments. The results show that the large deformation area, the region of high equivalent plastic strain and the void volume fraction coincide with the localized area. These phenomena are thought to be the precursor phenomena of shear banding. The width of the ligament of cracks and voids becomes narrower due to an increase in J, but it has a certain limit, and this result of analysis shows a quite similar tendency with the experiments.

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Behavior of Ductile Crack Initiation from a Notch under Mixed Mode Loading

Keiichiro TOHGO, Akio OTSUKA, Hong-Wei GAO

1988 Volume 37 Issue 419 Pages 885-890
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.885

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The behavior of ductile crack initiation from a notch under mixed mode loading has been investigated on a structural steel SM41A. Experiments and large deformation finite element analyses were carried out on the single edge notched specimens under various mixed mode loading conditions which were achieved by loading the appropriate positions in three-point bend tests and four-point shear tests. The profile of the notch tips deformed under mixed mode loading consisted of a sharpened part and a blunted part, and the latter part showed the highest void volume fraction in the notch tip region. The ductile cracks initiated from the mixed mode notch were of two types-fibrous type and shear type-depending on the loading mode. In the notch under mode I predominant-mixed mode loading, the fibrous type crack was initiated by coalescence of voids at the blunted part of the notch tip. On the other hand, in the notch under mode II predominant-mixed mode loading, the shear type crack initiation occurred by large shear deformation at its sharpened part. The initiation of the fibrous type crack from the mixed mode notch can be predicted by the critical void volume fraction at the notch tip. However, the shear type crack initiation is controlled by another criterion. Further study is needed to predict the initiation of the shear type crack from the mixed mode notch.

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Prediction of Dynamic Fracture Toughness Using Small Specimens

Yasuhiko TANAKA, Tadao IWADATE, Komei SUZUKI

1988 Volume 37 Issue 419 Pages 891-896
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.891

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The dynamic fracture toughness is the most critical parameter for the safety assessment of reactor pressure vessels. However, the measurement of the dynamic fracture toughness is very difficult because a special testing facility is required. For engineering use, the development of a method to predict the dynamic fracture toughness from small specimen tests is now strongly desired. One representative method for this aim is to use the correlation between the drop weight NDTT and the dynamic fracture toughness K_Id as set forth in ASME Code. However, the correlation does not work well because of difficulty in establishing an accurate one by scattering of NDTT due to the bead application on the drop weight specimen and by scattering of K_Id in the fracture toughness transition region. In this study, by taking account of these sources of scattering, the relationship between NDTT and dynamic fracture toughness was re-examined. The results revealed its definite dependence on the strength of the material used. On the other hand, the correlation between the Charpy index temperature and K_Id was not sensitive to the strength. This fact demonstrates the advantage of using FATT as the reference temperature to construct a master curve to predict K_Id. By using the data obtained, a single master curve, which can be used to predict the dynamic fracture toughness from the Charpy V-notch impact test results, was established for A508 Cl.3 and A533 Gr.B Cl.1 steels.

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Prediction of Fracture Toughness of Steels by Local Fracture Criterion

Takashi MIYATA, Akio OTSUKA, Masahiko MITSUBAYASHI, Toshiaki HAZE, Shy ...

1988 Volume 37 Issue 419 Pages 897-903
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.897

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Fracture toughness of a material is determined by its fracture characteristics as well as its plastic flow properties which control the stress-strain state at the crack tip.
The maximum tensile stress criterion is usually supposed as the fracture criterion for cleavage fracture of steels. So it was assumed in this study that cleavage fracture at the crack tip is initiated when the stress at a certain characteristic distance from the crack exeeds a certain limit. Based on this fracture criterion, the fracture toughness for cleavage fracture initiation can be given from the HRR solution by
J_c=C(n)X₀σ_ys(σ_c/σ_ys)ⁿ⁺¹
where σ_c is the cleavage fracture stress, C(n) is a function of strain hardening of materials, σ_ys is the yield stress and X_o is the characteristic distance.
By the use of this relation, the correlations have been obtained between the fracture toughness and flow/fracture properties of the materials, σ_ys and σ_c, obtained by the smooth and notched round bar tensile tests. A good agreement has been shown between these predictions and experiments on 8 kinds of low carbon structural steels which have various microstructures with the yield strength ranging from 280MPa to 1110MPa.

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Effects of Artificial Crack Length and Specimen Size on Bending Strength and Fracture Toughness of Hot-Pressed Silicon Nitride

Shoji HARADA, Naoaki NODA, Tatsuo ENDO, Mitsuyoshi NAGANO

1988 Volume 37 Issue 419 Pages 904-909
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.904

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Three-point bending and fracture toughness tests were conducted on two kinds of hot-pressed silicon nitride. To examine the size effect on the bending strength, two kinds of different sized specimens were prepared. The bending strength of the large specimens showed a lower mean value and a larger scatter than that of the small specimens. The Weibull statistics gave insufficient explanation on these differences because the Weibull modulus differed depending on the specimen size.
For the fracture thoughness tests, a semicircular crack with a radius of 50μm to 1400μm long was introduced on each specimen surface with the aid of Knoop indentation. The relationship between the fracture stress σ_F and the Knoop-indented crack length 2c was examined. Up to a critical value of 2c_c, σ_F was insentive to 2c. For 2c>2c_c, σ_F decreased with increasing 2c. The value of 2c_c differed depending on the materials. The fractographic observation revealed that for 2c<2c_c, the fracture origin was mostly located either at inclusions or defects.

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Measurement of Dynamic Fracture Toughness of Ceramic Material at Elevated Temperatures by Impact Test with Free End Bend Specimen

Masaru SAKATA, Sigeru AOKI, Kikuo KISHIMOTO, Yousuke FUJINO, Tooru AKI ...

1988 Volume 37 Issue 419 Pages 910-915
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.910

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A new instrumentation system was developed for the measurement of dynamic fracture toughness of ceramic materials at elevated temperatures up to 1200 deg C by impact test with a free end bend specimen (one-point-bend specimen). The specimen was of Charpy type (6mm width, 8mm height and 50mm length) made of silicon carbide (SiC) and a notch of 0.2mm width was cut by a diamond wheel. The specimen was hanged in an infrared image furnace by a couple of thin ceramic threads cemented onto the end surfaces of the specimen. Thus the heat conduction that usually takes place through support structure could be avoided or kept to a minimum. The impact force was provided by a falling steel cylinder of 6mm dia and 1500mm length with a pair of semiconductor strain gauges cemented onto a cylindrical surface to measure the stress wave history and hence to determine the impact force. Since the thin threads are thought to be broken at the moment of impact, the specimen is supposed to fracture without any constraint at both ends.
A simple formula was employed for determining the dynamic stress intensity factor from the measured impact force with a microcomputer used for processing the experimental data. A series of impact tests were performed with drop-height increased gradually and the dynamic fracture toughness was determined from the test data of the minimum drop-height that caused specimen fracture.
The dynamic fracture toughness values obtained by the impact test were compared with the results of quasi-static tests. It was shown that the developed system is satisfactory for measuring the dynamic fracture toughness of ceramic materials at elevated temperatures.

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Estimation for Fatigue Crack Opening Stress by FEM Analysis

Yoshihiko MUKAI, Arata NISHIMURA

1988 Volume 37 Issue 419 Pages 916-921
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.916

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Recent researches have clarified that the fatigue crack propagation rate has a good relationship with the effective stress intensity factor range (ΔK_eff). In order to estimate ΔK_eff, however, the fatigue crack opening stress level must be known. Surely, by using the FEM analysis, it is possible to calculate the opening stress, but the calculated value is affected by the minimum mesh size used in the analysis or stress range etc..
In this report, the new method for estimating the crack opening stress unconditionally from the calculated residual stress distribution was proposed, and the relation between crack opening stress and stress ratio (R≥0) was investigated based on the cyclic elasto-plastic analysis by FEM. The process of the proposed method was as follows: By using the compressive stress transmitted region on the crack plane and the total compressive stress obtained by FEM analysis, a certain ideal stress distribution on the crack plane was determined, and K value when the same stress distribution was applied on the crack plane was calculated (K^*_res1). On the other hand, from the stress distribution normalized so as that the loading direction stress of the element involving crack tip became the yield stress, another K value was calculated on the same process mentioned above (K^*_res2). K^*_res2/K^*_res1 was adopted as a correction factor, and K^*_res·K^*_res2/K^*_res1 was determined as K value at crack opening. (K^*_res was obtained by a superposition model.)
As the results, it was recognized that the proposed method gave about the same result under different mesh devisions or stress ranges. And also, the following relationship between the opening stress and stress ratio was obtained.
σ^*_op/Δσ=U₀-0.396R+R/(1-R)
where σ^*_op is the crack opening stress, Δσ is the stress range, R is the stress ratio and U₀ is the experimental value of σ^*_op/Δσ under R=0. It was also clarified that the above equation has a good agreemeat with the experimental results.

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A Simple Method of Evaluation for the Distribution of Fatigue Crack Propagation Life

Han Yong YOON, Hiroyuki OKAMURA

1988 Volume 37 Issue 419 Pages 922-927
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.922

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In order to understand the probabilistic nature of fatigue crack propagation, not only the calculation of failure probability and parameter sensitivity, but also the clarification of probabilistic nature of various parameters should be executed. Therefore a method to evaluate generally the effect of each parameter on the distribution of fatigue crack propagation life is reqired.
In this study, the system for evaluating the distribution of fatigue crack propagation life is developed on a micro-computer. By this system, a phenomenon of failure probability can be easily understood using the graphic representation and the dialogue style access. The effect of parameters on the distribution of fatigue crack propagation life can be discussed generally according to the appropriate normalization of the life distribution. The validity of this method is also shown.
Such an investigation as the present work is very simple but may be useful to understand the nature of the life distribution and to utilize the probabilistic fracture mechanics.

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Prediction of Elastic-Plastic Fatigue Crack Growth Rate and Crack Closure under Varying Loadings

Masahiro JONO, Atushi SUGETA, Hikaru OKADA

1988 Volume 37 Issue 419 Pages 928-933
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.928

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Load-controlled fatigue crack growth tests were carried out on two kinds of steels, S35C and SM50A, under constant amplitude loading and repeated two-step loading over a wide range from the linear elastic region to the post-yield one, and crack closure was investigated by using the minicomputer-aided unloading elastic compliance method.
The fracture mechanics parameter, ΔJ/E(1-J_max/C), was found to be a good parameter in expressing the fatigue crack growth rate under constant amplitude loadings irrespective of the stress ratios and materials, where ΔJ, J_max, E and C are the J integral range, the maximum J integral, elastic modulus and a constant related to fracture toughness, respectively. However it was found that the constant, C, was not related to the elastic-plastic fracture toughness, J_Ic, but to the fracture toughness, J_c obtained using the same geometry specimens with identical crack length.
The fatigue crack growth rate under repeated two-step loadings where both one-directional and cyclic plastic deformation were observed remarkably, could be well predicted by the linear summation rule of crack growth by using ΔJ^*/E(1-J_max/C), where ΔJ^* is the J integral range-pair taking account of one-directional deformation under low-level loadings.

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Evaluation of Fracture Mechanics Characteristics of a High Strength Graphite IG-11

Hideo KOBAYASHI, Yoshio ARAI, Haruo NAKAMURA, Tooru ARAKI, Tatsuo OKU

1988 Volume 37 Issue 419 Pages 934-938
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.934

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Fracture toughness and crack growth characteristics of stress corrosion cracking and fatigue were investigated for an isotropic fine grain size graphite, IG-11, one of the candidates for the core components of High Temperature Gas Cooled Reactors. The results obtained are summarized as follows:
(1) The fracture toughness and the fracture resistance were reasonably described by using the stress intensity factor. Introduction of the J-integral as a parameter did not bring an increase in accuracy.
(2) The plain strain fracture toughness K_Ic values for the fatigue precracked specimens were 0.93-1.00MPa√m. Without fatigue precracking, 10-20% decrease in fracture toughness was observed. In both cases, further crack growth brought an increase in the fracture resistance K_R up to 1.05-1.25MPa√m.
(3) The stress corrosion cracking did not occur in the material tested. On the other hand, the fatigue crack growth below K_Ic was observed although the crack growth mechanism is quite different from that for conventional metallic materials.

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Static and Cyclic Fatigue of Precracked Ceramics at Room Temperature

Takashi KAWAKUBO, Akira GOTO

1988 Volume 37 Issue 419 Pages 939-944
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.939

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The static and cyclic fatigue behaviors of alumina, silicon carbide, silicon nitride and partially stabilized zirconia were investigated at room temperature. Flexural specimens, with an indentation induced flaw at the center of each specimen, were tested under cyclic and static loads applied by four-point bending. All ceramics showed static and cyclic fatigue susceptibility. The fatigue degradation compared to its flexural strength increased in this order; silicon carbide, silicon nitride, alumina and partially stabilized zirconia. The cyclic fatigue strength of zirconia became as small as one-third of its flexural strength. Moreover, the fracture mode for the static and cyclic fatigue in zirconia was the mixed type of transgranular and intergranular cracking, although the intergranular cracking was dominant in the fast fractured portion. Between the static and cyclic lifetimes, little difference was observed in silicon carbide. However, a small acceleration by cyclic loading was observed in alumina at a relatively low applied stress, and a large acceleration was obtained in silicon nitride and in partially stabilized zirconia. The conventional fatigue theory, where the crack growth rate is time-dependent only, was not applicable in these materials. This acceleration by the cyclic loading is considered to be a result of the interaction between fatigue crack and microstructure, such as an interlocking effect against intergranular cracking in elongated columnar polycrystals of silicon nitride, and a transformation and microcracking in the process zone for partially stabilized zirconia. These interactions improve fracture toughness but cause a non-linear fracture behavior, and thus cyclic fatigue damage is accumulated due to stress hysteresis in cyclic loading.

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Quantitative Estimation of the Effect of Stress Rising, Holding and Descending Time on Fatigue Crack Growth Rate under Corrosion Environment

Toshimitsu YOKOBORI, Noboru CHIBA, Tetsuya YAMADA, Tomokazu KOSUMI, Ta ...

1988 Volume 37 Issue 419 Pages 945-950
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.945

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The corrosion fatigue tests were carried out for Cr-Mo steel (SCM440) by varying the stress rising time (t_R), holding time (t_H) and descending time (t_D). In the present paper, for the case of symmetrical stress wave (t_R=t_H), the constitutive equation of corrosion fatigue crack growth rate, da/dN|_CF, was derived explicitly in terms of t_R and t_H as follows:
da/dN|_CF=Dda/dN|_air, D=1/1-dt_R^et_H^fΔK^bexp{a(lnΔK)²+c} (1)
where da/dN|_air is the fatigue crack growth rate in air, ΔK is the range of stress intensity factor, a, b, c, e, and f are constants. The acceleration coefficient with holding time D(=[D]_{t_H}) is this equation was derived by the following method; First, the acceleration coefficient under the condition without holding time, [D]_{t_H=0} was obtained as:
[D]_{t_H=0}=a(lnΔK)²+blnΔK+c (2)
Next, under the condition with holding time, the holding time effect was estimated by the following equation,
[D]_{t_H}-[D]_{t_H=0}/[D]_{t_H}=dt_R^et_H^f (3)
The experimental results of corrosion fatigue crack growth rate under various stress rising and holding time conditions were found to be well expressed by eq. (1). On the other hand, this equation does not satisfy the critical condition that da/dN should be proportional to 1/t_H for t_H→∞, which is characteristics of stress corrosion cracking. Thus a more satisfied constitutive equation was derived as the equation of the following type: da/dN=F₀(ΔK, t_R, 2t_R+t_H). From this equation, it can be found that the corrosion fatigue crack growth rate is affected by f=1/(2t_R+t_H)) which concerns the time dependent effect and t_R which concerns the fatigue effect under the symmetrical stress wave condition.
Furthermore, it was deduced that the mechanism of the t_R process is controlled by the fatigue effect coupled with the time dependent effect controlling the t_H process, while the t_D process is controlled mainly by the time dependent effect although it includes some fatigue effect.

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Fatigue Crack Growth and Its Threshold in the Creep Regime

Kiyotsugu OHJI, Shiro KUBO, Hidenori KINUGASA, Tetsuyuki GOTOH

1988 Volume 37 Issue 419 Pages 951-956
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.951

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An experimental study was made on fatigue crack growth in SUS304 stainless steel at 650°C for stress ratios R in the range of -0.2≤R≤0.4. The behaviors of near-threshold fatigue crack growth and the associated crack closure in this range were compared with those obtained previously for R≤-0.4 and 0.5≤R. The crack closure was observed for -0.2≤R≤0.4 under the creep-fatigue conditions employed. The R value had a significant effect on the relationship between the cycle-dependent crack growth rate da/dN and stress intensity range ΔK as well as on the value of fatigue crack growth threshold ΔK_th for -0.2≤R≤0.4. When the J-integral range ΔJ_{f, eff}, in which the effect of crack closure was taken into account, was used instead of ΔK, the R dependence was eliminated, and the da/dN-ΔJ_{f, eff} relationship and the threshold value (ΔJ_{f, eff})_th were consistent with those obtained under 0.5≤R and R≤-0.4.
To investigate the character of the fatigue crack growth threshold in the creep regime, crack growth experiments were made using two-step varying loads, in which high load-range blocks were introduced periodically in sub-threshold low load-range sequences. To exclude the effect of crack closure, high stress ratios were employed. It was found that, when the number of load excursions in the high load-range block used in the experiments was small, the threshold was extinguished: cracks grew even under load-ranges lower than the threshold value obtained under constant-amplitude loading conditions. A modified Miner's rule was found to give a reasonable estimate of the crack growth rate under two-step varying loading conditions.

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Measurement of J-Integral Using Stress and Strain Fields Near a Crack Tip

An Application of the Computer Picture Processing

Naoki SONEDA, Shinobu YOSHIMURA, Genki YAGAWA

1988 Volume 37 Issue 419 Pages 957-963
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.957

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Currently, J-integral proposed by Rice is one of the most effective elastic-plastic fracture mechanics parameters. However, only a few experimental method, which restrict specimen's shape, have been developed for the evaluation of the J-integral. Some of them are Rice's formula for three point bend specimens, Merkle-Corten's formula for CT specimens and so on, which utilize a load vs. Load-point-displacement curve. The others are strain gauge methods, in which elastic strains around a crack are measured by many strain guages, and the J-integral is calculated by a contour integration technique.
In this study, we propose a new measuring method of the J-integral for arbitrarily shaped specimens. In this method, the displacement field in an elastic-plastic region near a crack tip is measured by a computer picture processing technique. Then the strain field is calculated by differentiating the displacement field, and the corresponding stress field is calculated using the multi-axial stress-strain relation of the deformation theory of plasticity. Finally the J-integral is evaluated through a contour integration technique. Since the present method directly measures the displacement field near the crack tip and evaluates the J-integral in the similar fashion to the numerical analyses, it can be applied to arbitrarily shaped specimens.
In this paper, after summarizing the displacement measurent process by the computer picture processing, the calculation method of the J-integral is described. Then the accuracy and applicability of the present method is discussed in detail by comparing it with the conventional procedure based on Merkle-Corten's formula in a tensile experiment of CT specimen.

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Detection of Configuration of Surface Cracks at Inside Surface of a Pipe from Outside Surface by DC Potential Drop Method

Makoto HAYASHI, Masahiro OHTAKA, Terunobu KOIKE, Norimasa CHIBA, Koich ...

1988 Volume 37 Issue 419 Pages 964-970
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.964

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The configuration of surface cracks has been detected by Direct Current Potential Drop Method (PDM). A simplified method for determining the reverse-face crack configuration was invented based on the FEM analysis of electrical fields near the surface cracks with different aspect ratios and depth. Here, the reverse-face crack is defined as the crack existing on the opposite side of the detecting surface of structural material, while the crack detected on the same side is defined as the surface crack. The newly developed method was applied to the detection of the fatigue cracks on the inside surface of 2 inch stainless steel pipes subjected to tensile cyclic stress. The potential difference distribution near the surface cracks was measured by using many potential difference measuring electrodes placed along the reverse-face cracks on the outside surface of the pipes with the same spacing as the wall thickness. The potential difference distribution obtained by the present simplified method showed that the reverse-face crack configuration could be determined with relatively good accuracy, if the crack depths were more than 30% of the wall thickness. Thus, the potential drop method is considered to be appropriate for an on-line monitoring system of the reverse-face cracks.

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Advanced Methods of X-Ray Stress Measurement Today

4. Applications of X-Ray Stress Measurement (II)

T. Hanabusa

1988 Volume 37 Issue 419 Pages 971-977
Published: August 15, 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.971

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Erratum to : Difference in Fatigue Crack Propagation Behavior at Stage II between Spheroidal Graphite Cast Iron and High Strength Steel

1988 Volume 37 Issue 419 Pages 982a
Published: 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.419_982a

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Erratum to : Experimental Determination of Elastic Constants of Granite as an Anisotropic Body

1988 Volume 37 Issue 419 Pages 982b
Published: 1988
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.37.419_982b

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