Journal of the Society of Materials Science, Japan

A Measuring System for Dynamic Stress Intensity Factors Using a FFT Analyzer

Application to Drop Weight Impact Three Point Bend Testing

Kikuo KISHIMOTO, Masaaki KURODA, Shigeru AOKI, Masaru SAKATA

1986 Volume 35 Issue 395 Pages 850-853
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.850

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Evaluation of the dynamic stress intensity factor K_I(t) is especially important in impact fracture toughness testing, since K_I(t) is influenced by the inertia force of a specimen and quasi-static estimation of K_I(t) usually leads to erroneous results.
In the present paper, a procedure is presented for measuring K_I(t) in the impact three-point bend testing. The contact force between the impactor and the specimen is computed first by using the output signal of a strain gauge mounted on the impactor and the transfer function of impactor. The FFT (Fast Fourier Transform) analyzer is utilized for measuring the transfer function in the pre-experiment in which the impactor is struck by a steel sphere and the impact force is measured by a piezoelectric accelerometer pick-up attached to the sphere. The time variation of K_I(t) is then determined by the computed contact force and a simple formula which has been derived previously by the present authors using Timoshenko's beam theory.
A program to run on a microcomputer was developed and assessment tests were conducted for the case that a steel or aluminum alloy specimen was impacted by a falling cylinder. Good agreement was obtained between the computed K_I(t) and the value determined from the strain gauge mounted near the crack-tip.

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Finite Element Analysis of Dynamic Three Point Bending Test Considering Contact and Frictional Effects

Yasuhiro KANTO, Genki YAGAWA

1986 Volume 35 Issue 395 Pages 854-859
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.854

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Dynamic three point bending test is one of the general methods to test the dynamic fracture characteristics of materials. However, it is generally hard to measure the dynamic load generated by interaction of two bodies. In order to make it easier in the test, many impact methods, such as the one using a rod-impactor to measure the dynamic load from its response and that using the electro-magnetic force instead of the impactor loading, have been proposed.
In addition, the evaluation of the dynamic fracture mechanics parameter is also difficult. Many researchers are using the static calibration between the load and K_I value. However, it has been also reported that the load doesn't have good correlation to the dynamic stress intensity factor. Therefore, a detailed simulation is necessary to evaluate the methods of obtaining the dynamic stress intensity factor.
In this study, the finite element analysis of dynamic three point bending test using a rod-impactor, by which the dynamic load can be measured easily, was made with consideration of the contact-separate behavior and frictional effect at the loading and support points. The stress intensity factors evaluated by several methods were compared. The following results were obtained.
(1) K_I values calculated by the static load-K_I relation had a larger oscillation than those by other methods. In addition, the non-zero frictional coefficient caused the reductions in displacement, COD_mouth and J-integral, but did not affect the load. From these points, the method using the static load-K_I relation is not appropriate for this case.
(2) As the ratio of the span to the width of the specimen (S/W) became smaller, the oscillation of the time history of K_I value and the separation between the specimen and the support became less.
(3) The lower modes of vibration were dominant in the response of the specimen in spite of impact loading.

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Crack Arrest Behavior of Fast Fracture in Steel

Susumu MACHIDA, Hitoshi YOSHINARI, Akihito YAHIRO

1986 Volume 35 Issue 395 Pages 860-866
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.860

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The concept of crack arrester, such as the insertion of a high toughness plate, is an effective means to avoid the catastrophic brittle fracture in welded steel structure. Many researches have been made to clarify the arrest behavior of brittle fracture and to establish the arrester design concept, but an inadequacy still exists in the arrest theory.
In this study, three types of crack arrest tests, i.e. temperature gradient type double-tension test, stress gradient type double-tension test and surface notched double-tension test were carried out by using mild steel. The data obtained were analyzed from the standpoint of the energy balance concept on the basis of dynamic fracture mechanics.
Shear lips which are related to plastic deformation around a propagating crack tip were found to contribute to crack arrestability of steel because they can absorb rather a large amount of energy. And the dynamic fracture toughness K_D^b corresponding to a brittle fracture surface, which can be evaluated by subtracting the contribution of shear lips from the total absorbed energy, seemed to be defined as a function of crack speed and temperature. Thus, K_D^b is a material quantity and the arrest behavior of brittle crack may be interpreted generally by this value.
Further work to find out the conditions controlling shear lip formation is necessary for the prediction of crack run/arrest phenomenon.

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Ductile Crack Initiation and Void Volume Fraction

Investigation Based on Gurson's Yield Function

Akio OTSUKA, Keiichiro TOHGO, Yoshihide OKAMOTO

1986 Volume 35 Issue 395 Pages 867-872
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.867

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

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Prediction of Fracture Toughness K_Ic of Steel from Charpy Impact Test Results

Tadao IWADATE, Yasuhiko TANAKA, Hiroyuki TAKEMATA, Shuhei TERASHIMA

1986 Volume 35 Issue 395 Pages 873-879
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.873

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This paper presents a method to predict the fracture toughness K_Ic and/or K_Id of steels using their Charpy impact test results and tensile properties. The fracture toughness, Charpy impact and tensile properties of 21/4Cr-1Mo, ASTM A508 Cl.1, A508 Cl.2, A508 Cl.3 and A533 Gr.B Cl.1 steels were measured and analysed on the basis of the excess temperature (test temperature minus FATT) and Rolfe-Novak correlation. The relationship between K_Ic/K_Ic-us and the excess temperature, where K_Ic-us is the upper-shelf fracture toughness K_Ic predicted by Rolfe-Novak correlation, discloses that the K_Ic transition curves of several steels are representable by only one trend curve of K_Ic/K_Ic-us or K_Id/K_Id-us versus excess temperature relation. This curve is denoted as a “master curve”. By using this curve, the fracture toughness of steel can be predicted using Charpy impact and tensile test results. By taking account of the scattering of both the fracture toughness and Charpy impact test results, the confidence limits of the master curve were also determined. Another approach to develop more general procedure of predicting the fracture toughness K_Ic is also discussed.

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Study on Fracture Condition of Biaxially Loaded Connections in Steel Structure

Tadao NAKAGOMI, Tomoji IIJIMA, Susumu MINAMI

1986 Volume 35 Issue 395 Pages 880-886
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.880

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It is considered that the fracture of beam-to-column connections in steel structures occurs after the slow crack growth, when structures are subjected to repetitive large strains such as a strong earthquake exciation.
The purpose of the present experiments and analysis was to investigate the influences of fracture toughness, temperature and stress distribution on their fracture conditions. This paper deals with the investigation on fracture of subassemblages including beam-to-column connections with notch and lamination under biaxial force. The axial stress ratio (axial stress of column/yield stress) was varied. The model was analyzed by using the elasto-plastic finite element method. The results of the analysis and the experiments are as follows.
J-integral of these analytical models was influenced by the axial stress which is parallel to the crack; the higher the compressive axial stress of column, the larger the value of J-integral. The fracture of specimens made of low fracture toughness steel can be explained by J_Ic fracture criterion. For steel of high fracture toughness, however, it is necessary to consider not only J-integral but also other fracture conditions such as elastic strain energy for brittle fracture after slow crack growth.

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Study of Fracture Toughness of Columnar Grained Ice Using Large Specimens

Sho KUSUMOTO, Nobuo KIMURA, Tooru TAKASE, Tohru KIDERA

1986 Volume 35 Issue 395 Pages 887-891
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.887

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The effects of loading rate and specimen size on the fracture toughness K_Ic of columnar grained ice have been investigated at -10°C. Notched bend specimens with the section size of 50×50mm (medium size specimen) and 200×50mm (large size specimen) were used. The notch of specimen was made using a thin razor blade embedded in the mold. Several tests were carried out at each test condition, and probabilistic nature of fracture toghness was also investigated.
The results obtained are as follows.
(1) The value of K_Ic decreased as K_I increased, and there was a transition in the range of K_I≈10-100kPam_1/2/s. The value of K_Ic was not substantially affected by K_I in the high K_I region beyond the transition.
(2) Scatter of K_Ic for the large size specimens was considerably small compared with that for the medium size specimens.
(3) The minimum value of K_Ic was not affected by the specimen size in the low K_I range. However, in the high K_I range, the minimum value of K_Ic of a large specimen showed a little higher value than that of a medium specimen.
(4) The size effect was analyzed from the view point of the “weakest link theory”. It was observed that the experimental data did not agree with the theoretical prediction in the range of low values of K_Ic.
(5) The relation between K_I and K_Ic was compared with other experimental data on a similar kind of ice. Considerable difference in K_Ic, especially in the low loading rate range, was observed. The reason is not yet clear, and more studies are needed.

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Evaluation of Fracture Toughness for Ceramics by Chevron-Notched Specimen

Hideo KOBAYASHI, Haruo NAKAMURA, Atsushi KITAYAMA, Satoshi OHOTE

1986 Volume 35 Issue 395 Pages 892-897
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.892

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Chevron-notched specimens are being used recently to determine K_Ic. In this study, the stress intensity factors were calculated for chevron-notched three point bend and compact specimens. Three configurations of chevron-notched specimens were then subjected to fracture toughness tests to determine K_Ic of hot-pressed silicon nitride, Si₃N₄, with special attention paied to the fracture resistance curve (R-curve). Using this result, the optimum shape of the specimen was determined.
The results obtained are summarized as follows.
(1) By using the deeply chevron-notched specimen, K_Ic can be determined in a simple way with little scatter.
(2) The K_Ic values determined by using the straight-notched specimens show a considerable scatter due to the effect of finite notch root radius and they overestimate the actual K_Ic value.
(3) From the change in specimen compliance, the R-curve can be evaluated. The resistance to stable crack growth increases slightly as the crack grows.

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Evaluation of Crack Propagation in Ceramics by Double-Torsion

Fumihiro WAKAI, Hisashi SAKURAMOTO, Shuji SAKAGUCHI, Yosoo MATSUNO

1986 Volume 35 Issue 395 Pages 898-903
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.898

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In ceramics, delayed failure occurs due to slow growth of preexisting cracks by stress corrosion. Such subcritical crack growth in high performance ceramics should be characterized for their life prediction based on fracture mechanics. In the present study, the effect of environment on the stress intensity factor (K)-crack velocity (V) relationship was studied for various high performance ceramic materials. The double torsion (DT) method that utilizes the load relaxation technique was employed for the determination of K-V characteristics.
Three regions were distinctly observed in the K-V diagrams not only for oxide ceramics, such as alumina and yttria-partially stabilized zirconia (PSZ), but also for non-oxide ceramics, sintered and hot-pressed silicon nitride. In water, straight lines corresponding to region 1 were obtained. The position of region 2, in which crack velocity is controlled by diffusion of corrosive species, depended on the amount of water in air and toluen. Stress corrosion of silicon nitride by water is believed to be caused by the presence of residual oxinitride glass phase at grain boundaries. The mechanism of stress corrosion by water was discussed on the basis of chemical bond rupture model.
Acoustic emission caused by crack propagation was also studied for PSZ and sintered silicon nitride. The amplitude of acoustic emission event was dependent on crack velocity for sintered silicon nitride, but independent for PSZ.

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Small Fatigue Crack Growth at Notch Root in Elastic-Plastic Range

Izuru NISHIKAWA, Masuo KONISHI, Yoshio MIYOSHI, Keiji OGURA

1986 Volume 35 Issue 395 Pages 904-910
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.904

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The growth and closure behavior of a small crack initiated at a notch root was investigated for SUS 304 and SM41A steels under the situation of enhanced notch plasticity. An acceleration of growth rate as well as an increase in crack-opening range were observed for a small crack which was embedded in the notch-plastic zone. All of the growth data for the small crack at the notch root were successfully correlated with those for long cracks by the effective stress intensity factor range, ΔK_eff. ΔK_eff was found to be a controlling parameter for crack growth up to higher nominal stress range, as far as the crack closure was observed and the notch-root plastic region was surrounded by the elastic region. A primary controlling factor for the closure of the small crack at the notch root was found to be notch-root plasticity. This was supported by the analytical study by using the finite element method.

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Effects of Hardness and Crack Geometry on ΔK_th of Small Cracks

Yukitaka MURAKAMI, Masahiro ENDO

1986 Volume 35 Issue 395 Pages 911-917
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.911

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The dependence of ΔK_th on crack size and material properties under stress ratio R=-1 was studied on various materials and microstructures. The values of ΔK_th for all the materials investigated were standardized with one geometrical and one material parameter.
The geometrical parameter, √area, is the square root of the area which is occupied by projecting defects or cracks onto the plane normal to the maximum tensile stress. The relationship between ΔK_th and √area is expressed as follows:
ΔK_th∝(√area)^1/3 (a)
The most relevant material parameter to standardize the data was the Vickers hardness, and the following relationship was obtained:
ΔK_th∝(H_V+C) (b)
The constant C in Eq. (b) reflects the difference of nonpropagation behavior of small cracks in soft and hard metals.
By combining Eqs. (a) and (b), the following equations were derived for predicting ΔK_th and the fatigue limit σ_ω of cracked members.
ΔK_th=3.3×10^-3(H_V+120)(√area)^1/3 (c)
σ_ω=1.43(H_V+120)/(√area)^1/6 (d)
where the units are ΔK_th: MPa·m^1/2, σ_ω: MPa, √area: μm and H_V: (kgf/mm²). Equations (c) and (d) are applicable to a crack having √area approximately less than 1000μm.

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Direct, Real Time Observation and Mechanism of Fatigue Crack Growth

Relation between Growth Rate and Crack Tip Opening Displacement

Masahiro JONO, Jiho SONG, Kunio GOTOH, Shinji YAMADA

1986 Volume 35 Issue 395 Pages 918-923
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.918

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Fatigue crack growth tests were performed on grain-oriented 3% silicon iron in a high-resolution, field emission type scanning electron microscope, using a specially designed servo-hydraulic fatigue loading system, and direct, real time observations of a growing fatigue crack were made.
Good correlation was found between crack growth rate, da/dn, and crack tip opening displacement, CTOD, under constant amplitude load testing. The ratio of growth increment to CTOD, however, was reduced with decrease of crack growth rate. Fatigue crack growth behavior and relation between growth rate and CTOD under Hi-Lo two step loading tests were also discussed.

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Near-Threshold Fatigue Crack Growth Behavior and Crack Closure under Creep Conditions

Kiyotsugu OHJI, Shiro KUBO, Yasuo MANABE

1986 Volume 35 Issue 395 Pages 924-929
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.924

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The fatigue crack growth behavior of SUS 304 stainless steel at 650°C was investigated under low stress ratios R on the basis of the non-linear fracture mechanics. Emphasis was placed upon the near-threshold fatigue crack growth behavior and crack closure under creep conditions. It was found that in the very low da/dN region and the high da/dN region the relation between the cycle-dependent crack growth rate da/dN and stress intensity factor range ΔK obtained for -1≤R<0.2 deviated from the same correlation obtained under 0.5≤R. The values of fatigue threshold ΔK_th for low R were much greater than those obtained for high R. Such a strong R dependence of the crack growth behavior found in the low R region was eliminated by the use of J-integral range ΔJ_{f, eff}, in which the effect of crack closure as well as that of material non-linearity were taken into account. The near-threshold crack growth behavior was found to be very sensitive to the loading history including frequency. This was rationalized in terms of the effect of oxide-induced crack closure enhanced by fretting as well as that of time-dependent creep deformation.

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Fatigue Crack Growth Rate and Crack Initiation and Fracture Life under Mixed Modes I and II

Toshimitsu YOKOBORI, Takeo YOKOBORI, Kenji ISHII, Kiyoshi SATO, Kazuo ...

1986 Volume 35 Issue 395 Pages 930-935
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.930

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The mixed mode fatigue testing was carried out by applying the same phase and arbitrary ratio of torsional loading to tensile loading.
The threshold stress intensity factor and fatigue fracture toughness decreased with an increase of ΔK_II0 for initial crack.
On the other hand, the stable fatigue crack growth region was found to be devided into II_a region of low growth rate and II_b region of accerated fatigue crack growth rate. Both regions were influenced by mixed mode loading.
The crack initiation life N_i and propagation life N_f had similar characteristic in terms of (1+Δτ/Δσ)/√ΔK_I0²+3ΔK_II0²=(1+ΔK_II0/ΔK_I0)/√ΔK_I0²+3ΔK_II0², where ΔK_I0 and ΔK_II0 are the stress intensity factor amplitude of initial crack. The value of N_i/N_f was found to be about 0.12.

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Detection of Configuration of Surface Fatigue Crack in Inside of Stainless Steel Pipe by DC Potential Drop Method

Makoto HAYASHI, Masahiro OHTAKA, Kunio ENOMOTO, Tsukasa SASAKI, Toshik ...

1986 Volume 35 Issue 395 Pages 936-941
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.936

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The configuration of surface fatigue cracks in 12 inch stainless steel pipes was detected by Direct Current Potential Drop Method (PDM). In the process, a simplified method for determining the surface crack configuration was invented based on the analysis of electrical field by FEM. First, the calibration curves of potential ratio V/V₀ vs. normalized crack depth a/t were made for every a/c=0.01 using the relation of potential ratio V/V₀ and crack aspect ratio for various crack depths. The crack depth was derived by substituting the maximum potential ratio measured at the crack center into an appropriate calibration curve. The calculated crack aspect ratio was compared with the crack aspect ratio of the calibration curve. If the former differed from the latter, the crack depth was evaluated by the calibration curve with another crack aspect ratio until both of the crack aspect ratio coincided. The whole crack configuration was determined by substituting the potential ratio measured at each position into the coincident calibration curve. The method was applied to the fatigue crack and the crack shape was estimated with the accuracy of ±0.3mm.

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Experimental Investigation on Two-Dimensional Crack Measurement by Electric Potential CT Method

Kiyotsugu OHJI, Shiro KUBO, Takahide SAKAGAMI, Takeshi HASHIMOTO

1986 Volume 35 Issue 395 Pages 942-947
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.942

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Practicability of the proposed electric-potential CT method for quantitative measurements of cracks was experimentally examined using steel plates with a two-dimensional crack. In thismethod, the observed values of electric potential distribution on the surface of a cracked body were computer-processed by an inverse numerical analysis to identify the location and size of two-dimensional cracks. As an inverse analysis scheme “the least residual method” was used in this investigation. This scheme involves boundary element analyses of electric potential for various assumed crack locations under given boundary conditions and comparison of these computed values with the observed values. The least residual criterion was used to find the most probable location of the crack. Experiments were performed for determination of location and size of two-dimensional cracks embedded in steel strips from the electric potential distribution along the side-faces. The location and size of short or long single-edge and internal cracks were determined with good accuracy, demonstrating the practicability of the proposed method.

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Fatigue-Foundamental Aspects Design Application

7. Modern Techniques for Fatigue Testing and Evaluation

M. Jono, K. Mori

1986 Volume 35 Issue 395 Pages 948-954
Published: August 15, 1986
Released on J-STAGE: June 03, 2009

DOIhttps://doi.org/10.2472/jsms.35.948

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