A history-dependent in-service inspection policy for fatigue crack growth processes was investigated based upon a stochastic fracture mechanics. A conditional reliability function was firstly evaluated from the time-dependent crack length density obtained previously, given that the component has not been exchanged until the time in question. With the aid of an idea of the renewal theory, a kind of functional equation to describe the reliability function was then set up on the assumption that components are exchanged as soon as cracks are detected. Lastly, the equation was numerically solved to clarify the effect of the policy on the reliability degradation.
This paper attempts to improve the fuzzy expert system which was previously developed by the authors for assessing damage states of RC (Reinforced Concrete) bridge deck. Using the concept of “damage mode”, it is possible to evaluate the remaining life of RC bridge deck. Moreover, it is intended to introduce the neural computing technique for the refinement or generation of fuzzy production rule. An illustrative example is presented to demonstrate the applicability of the system.
Crushing tests of ceramic bearing balls are usually carried out by compressing two balls of the same size against each other. In the conventional data analysis, it is considered that n pairs of balls yield the crushing load data of sample size n. In the present paper, a new method for data analysis was examined. In this method, it is considered that n pairs of balls yield the crushing load data of the sample size 2n of which about half are censored values. The new method is based on the experimental observation that one ball usually remains intact even if the other ball fails. Hence, the method seems to be more reasonable than the conventional method. Applying the new method to our experimental data reported in the previous paper, the followings were found: (1) a two-parameter Weibull distribution fitted well to the experimental data when analyzed by the new method as well as when analyzed by the conventional method, (2) the shape parameter by the new method was almost the same as that by the conventional method, and (3) the scale parameter by the new method was slightly larger than that by the conventional method, and the difference was only 5%. These results justify the use of the conventional method from a practical point of view. Furthermore, a theoretical analysis was performed, and the above results (1), (2) and (3) were found to agree with the theoretical predictions.
Recently, reliability assessment on the micro-joining for electronic apparatus attracts major attention of engineers and researchers in this field. Failure problems of the micro-joining have to be investigated from an interdisciplinary point of view, for the failure phenomena are caused not only by a mechanical effect but also by a metallurgical and/or electrochemical effect. For example, construction of brittle intermetallic compounds at Au wire/Al pad interface of ball bonding is a problem of metallurgical aspect, and electro-migration induced between soldering parts on high density printed circuit board is problem of electrochemical aspect. Though there are several micro-joining methods such as thermo-compression, ultrasonic bonding, micro-soldering and so on, a majority of micro-joining applied in electronic apparatus is micro-soldering. Therefore, it is an urgent problem to establish a valid evaluation method for solder joint performance under service conditions. A typical problem on this point is the solder cracking induced by temperature cycling, depending on the mismatch of thermal expansion coefficients of structural elements. In order to clear the failure problem of solder joint, fatigue failure mechanism of solder itself must be systematized. The main purpose of the present study is to investigate the fatigue strength and strain behaviors of 60Sn/40Pb solder plate specimen under several repeated load conditions including impact load carried out at room temperature. And furthermore, room temperature creep tests were also carried out to discuss the correlation between cyclic fatigue and static fatigue of the solder. The results of this study revealed a clear dependence of the fatigue life on the stress patterns; the lower was the frequency of stress cycle the lower was the fatigue strength. And the strength in impact fatigue showed the highest value. Then, the evaluation from the viewpoint of cumulative loading time indicated that the fatigue life of the solder could be well estimated by the cumulative loading time regardless of the type of stress pattern. And furthermore, the relationship of the stress vs. the cumulative loading time in cyclic fatigue well coincided with the creep rupture curve.
In order to clarify the effect of cycling frequency on the fatigue life of solder, strain controlled fully reversed torsional fatigue tests were carried out on thin-walled cylinder type 60Sn-40Pb solder specimens under six strain cycling frequencies of 0.001, 0.01, 0.03, 0.05, 0.5 and 1.0Hz at 303K. The results obtained in this study are summarized as follows: (1) As a general strength trend of the solder, the lower was the strain cycling frequency the shorter was the fatigue life. But, the solder showed an opposite strength trend in the inelastic strain range exceeding about 1.4%, presumably depending on the creep effect. (2) Two different expressions were constructed to evaluate the fatigue life of the solder under relatively high cycling frequencies over 0.03Hz, and under all cycling frequencies (0.001-1.0Hz), respectively. The expression for the former case was constructed on the basis of the Coffin's frequency modified fatigue life estimation method. And the expression for the latter case was a general one constructed by using the strain-range partitioning approach and linear cumulative damage concept to take account of the superposed effect of both plastic and creep deformations. The fatigue lives estimated by the above two expressions coincided well with the corresponding experimental results.
Epoxy resins used for encapsulating integrated circuit (IC) devices are filled with silica particles that have broadly distributed diameters, ranging in size from less than 1μm to about 100μm. Since the particles occupy 60 to 70% of the volume, they have a significant effect on the fracture properties of the resin. However, very little is known about the effect of particle-size distribution. In this study, the fracture toughness of silica particulate-filled epoxy resins, with eleven different particle-size distributions, was measured using the double torsion test. Polynomial regression analysis of the measured results was done on various definitions of mean particle diameters. It was found that the resin fracture toughness increases with increasing filler particle size. Scanning electron microscopy of the fracture surfaces indicates that a crack bypasses small particles less than about 5μm in diameter by propagating through the matrix around the particle, whereas it propagates through particles larger than about 30μm. The crack propagates along the particle/matrix interface for particle sizes in between these sizes. The best correlation with resin fracture toughness is obtained for the volume mean diameter of filler particles among various definitions of mean diameters. The effect of the volume mean diameter on crack propagation is explained in terms of filler particle distribution around the crack front.
Metal matrix composites (MMC) and aluminum alloy were examined by a scanning acoustic microscope (SAM) using leaky Rayleigh wave to discuss the analysis of deformation behaviour around reinforcing fibers of MMC. The plastic zone size observed was nearly equivalent to the one calculated under the plane stress codition for A6N01 aluminum alloy and the difference in Rayleigh wave velocity was about 2% between the plastic zone near a fatigue crack tip and the elastic zone. The deformation part at the tip of notch occurred preferentically in the SiC wisker poor zone for SiCw/A7075 composite. It is suggested that fatigue cracks initiate and propagate at the whisker poor zone for this composite. The microstructure such as segregation of elements or precipitates can be analyzed by using the velocity of leaky Rayleigh waves. It is suggested that the microstructure and plastic zone may be separately identified in MMC.
Dilatancy of rock is interpreted as the accumulation of microscopic failures induced by deviatric stress, based on a great number of experiment and observation. However, the ability to express the quantitative relationship between stress condition and dilatant strain caused by such micro-scopic failure requires more research. In this paper, on the assumption that open cracks grow in consequence of failures, the equations which describe the stress-strain relationship were derived by applying the fracture mechanics. The conclusions are summarized as follows; (1) Secondary cracks generated by deviatric stress grow almost in the direction of maximum compressive stress. (2) Dilatant strain caused by the crack growth is in inverse proportion to minimum compressive stress.
In order to make clear the strength development mechanism of intermediate soils, the direct shear tests were performed on artificially mixed soils to examine the influences of soil texture and consolidation pressure. The following conclusions were obtained: (1) The shear strength characteristic of soils changes from that of sand to clay with increasing clay content and from that of clay to sand with increasing consolidation pressure. (2) From the direct shear tests, the experimental constant cσc characterizing the boundary between sand and clay was found to exist and vary with the clay content and consolidation pressure. (3) The expreimental constant cσcn characterizing the soil properties was also found.
Morphology and preferential orientation of the rod-like α phase appearing during low temperature annealing of β' Cu-41.7% Zn alloys were investigated by SEM observation and SEM-ECP method. At the (111) plane of β' matrix, three groups of rod-like α phase intersected with each other at the angle of 60 degree between two of them. At the (001) plane of β' matrix, two groups of rod-like α phase intersected with each other at the angle of 90 degree between them. At the (011) plane of β' matrix, two groups of rod-like α phase intersected with each other at the angle of about 70 degree. In this case, another group which had shorter length than the other two groups was observed and it intersected with other groups at the angle of 55 degree. It was estimated that the rod-like α phase might be elongated preferentially in the ‹111› direction of β' matrix. But the exact preferential direction of the rod-like α phase was not determined in this investigation because a single rod of α phase could not be selected from a bundle of rods. Thus it was not possible to establish any strict orientation relationship between the rod-like α phase and the β' matrix. The length and radius of the lod-like α phase increased with increasing annealing time, and the activation energy for the growth of rod-like α phase was determined to be about 135-139kJ/mol.
Static and dynamic tensile tests for sintered tungsten alloys having various volume fractions of tungsten particles were carried out in order to investigate the effects of volume fraction of tungsten, loading rate and mean diameter of tungsten grain on the mechanical properties. Both the Young's modulus and the yield strength increased with increasing volume fraction of tungsten. The tensile strength became maximum at the tungsten volume fraction of 90%. The true fracture stress, elongation and true fracture strain were reduced with increasing volume fraction of tungsten. However, these mechanical properties were scarecely influenced by the mean diameter of tungsten grain in the range from 30.5μm to 39.4μm. Although the yield and tensile strengths varied a little in the strain rate lower than 1.0s-1, they increased remarkably with increasing strain rate in the strain rate region higher than 1.0s-1. According to SEM observation, the cleavage fracture facets increased with increasing fracture strain.
Mechanical properties of ceramics are sensitive to the microstructure of the machined surface. The fracture strength has been studied in the past as a function of surface roughness of ceramics, and it has been noticed that micro cracks exist in the ground surface layers. The microcracks caused by grinding abrasion, however, have not been clearly observed. The purpose of this study was to describe the micro-structure of ground surface of alumina ceramics and to obtain its influence on the bending and fatigue strengths. The following results are obtained. (1) According to TEM observations, both the inter- and the trans-granular fracture occurred in the surface layers. (2) Micro cracks developed in the area of trans-granular fracture. (3) The structure image of the strained area suggested that lattice deformation occurred when diamond grains hit an alumina grain. Some dislocations were also observed in the alumina grain. (4) The diamond grain size of the grinding wheel did not have so much effect on the three point bending strength. (5) The specimen ground by a #325 diamond grinding wheel showed slightly higher fatigue strength than by a #800 diamond grinding wheel.
The fracture strength of ceramic-metal bonded material is determined by the characteristics of its interface. In the case of the bonding attained by using insert metal such as Ag brazing, the yielding phenomenon would affect the stress singularity at the interface near the end position and its strength. In this paper, the effects of plastic deformation and layer thickness on the stress singularity and strength of the bonded joint were studied. The results obtained are as follows. The material dynamic role of soft insert metal was considered to relieve its stress singularity at the bonded interface. This effect became larger with decreasing thickness of insert metal. But when a large plastic deformation concentrated at the bonded interface, the fracture strength came down. This phenomenon seemed to be caused by the high normal stress acting to the interface, which was induced by the movement of slip lines being prevented by the bonded interface. In addition, the stress singularity was found to become smaller as the Young's modulus of the insert metal became higher.
Inhomogeneous deformation occurring at the interface of a laminated thin sheet is considered to be one of the mechanical behaviors causing interface fracture or determining its forming limit. The behavior of deformation such as interfacial roughening may also be related with the interfacial plastic instability. Experimental investigations on such deformation have been performed by using an aluminum foil laminated with a plastic film on each side and subjecting it to biaxial tension. This report puts an emphasis on the growth of interfacial roughening in comparison with the surface roughening in the aluminum foil alone subjected to the same tension. The relation between the growth of roughening and macroscopic fracture is also discussed. Two kinds of aluminum foils were supplied, one being pure aluminum with a certain grain size and the other aluminum alloy. The interfacial roughening was observed in-situ through an optical microscope and was measured at several strain levels from the cross sections of the laminate samples which were molded by resin. It was found that the interfacial roughening did not grow monotonically due to the hardening properties and the rigidity (thickness) of the skin material. It is also regarded as one of the characteristic features of fracture that the necking occurs in the aluminum foil after the delamination at the interface propagates up to a certain region.
Bearing strength of four pitch-based and two PAN-based carbon fiber composite materials of [0°/±45°/90°]3S laminate has been measured. The specimens, which had different bearing hole position and width, were prepared and tested to investigate the effects of geometrical parameters on the bearing strength and failure mode. The bearing strength was correlated with the mechanical properties of longitudinal reinforcing fibers and discussed based on the microstructural damage examination by using an optical microscope. The following concluding remarks were derived. (1) The full bearing strength was developed when the edge distance ratio, e/D, was equal to or larger than 3.0 and the side distance ratio, w/D, was equal to or larger than 4.0 for both high tensile and high modulus carbon fiber composite materials. (2) As the fiber strain to failure became higher and also as the longitudinal compressive strength of unidirectional composites became higher, the bearing strength became higher. No correlation was apparent between tensile strength of the fiber and the baring strength.
This paper presents an analytical method for predicting flexural damping capacity of laminated composite beams made of carbon fiber reinforced thermoplastics (CF/PEEK). The effects of fiber orientation angle, stacking sequence and the laminate geometry on flexural damping capacity and resonance frequency are discussed by decomposing the laminate energy dissipation associated with each of three resulting stress components. Each of the energy dissipation terms is then identified, and their effects on damping capacity are examined by calculating their contributions to the total laminated energy dissipation. For comparison with the analytical results, an experimental study for measuring damping capacity and resonance frequency of a cantilever laminated composite beam was carried out by an impulse-frequnecy response technique. A good agreement obtained between the analytical and the experimental results of off-axis and cross-ply laminates shows that the analytical method developed here is satisfactory for predicting flexural damping and resonance frequency.
Flexural fatigue tests were performed on three high modulus pitch-based carbon fiber (400, 500, 600GPa) unidirectional composites and a high modulus PAN-based carbon fiber one in order to investigate the effect of strong nonlinear elasticity on the compressive stress-strain relation of the pitch-based ones. In the test, the three-point flexural method was adopted with two stress ratios: R=0.05 and R=-1.0 (perfectly alternated loading). The test results showed that for both stress ratios the high modulus pitch-based carbon fiber unidirectional composites possessed as much fatigue durability as that of the high modulus PAN-based carbon fiber composites, though the pitch-based ones had stronger compressive nonlinearity than that of PAN-based ones. If the compressive nonlinearity were associated with fiber damage, the fatigue durability should be affected by the degree of nonlinearity. However, since this was not the case, it is considered that this nonlinearity in the high modulus pitch-based carbon fiber composites is not associated with fiber damage but is of an elastic nature.
In this paper, the effects of concentration and temperature on the propagation rate of stress corrosion crack were examined in cross ply glass/epoxy laminates exposed to acid environments. At first, stress corrosion crack tests were carried out on compact tension specimens of the laminates under various environmental conditions. After that, the propagation rate was evaluated theoretically by using the formura derived previously from the viewpoint of a micromechanics approach. Then, it has been found that the theoretical results agree almost well with the experimental ones. Thus, the effects of concentration and temperature on the propagation rate have been clarified quantitatively.
In the first part of the paper, the crack growth process in rolling contact fatigue has been investigated on ring type plate specimens, in which crack growth is two dimensional and cracks are observed on the side surface of the specimens. The results have shown that cracks are initiated from the contact surface in tensile mode in the direction approximately normal to the contact surface and after some short length of growth, shear mode growth occurs from the tip of the crack and it grows until the separation of the surface layer, namely flaking type failure, occurs. In the second part, mode II fatigue crack growth tests have been made by using an apparatus designed based on the concept that the subsurface fatigue crack growth in rolling contact fatigue is the mode II fatigue crack growth under the stress state where the tensile mode growth is suppressed by compression stress field. The test results have shown that the mode II fatigue crack growth occurs in steel if the superposed compression stress is enough to suppress the tensile mode growth.
Many machine and structural materials have strain rate dependence at room temperature. In such material, fatigue strength, that is, fatigue crack initiation life and propagation rate more or less depend on stress frequency. However, in many cases, the effect of stress frequency was almost all ignored and fatigue strength was evaluated based on the results of fatigue test under a constant loading frequency. Such evaluation is likely to over/under estimate fatigue strength. So, in strain rate dependence materials, the study made clear the effect of stress frequency on surface crack propagation by the following experiments and analysis. (1) Evaluation of strain rate dependence of material. (2) Making clear the effect of loading frequency on surface crack propagation by fatigue test and observation of fracture surface by SEM. (3) 3D-elasto/visco-plastic FEM simulation of surface crack propagation. (4) Comparison of the experimental results with the calculation ones by FEM, and establishment of an evaluation's parameter describing the effect of stress frequency on surface crack propagation. The results obtained are summarized as follows; (1) In strain rate dependence materials, the surface crack propagation rate and striation space depend on stress frequency. (2) The effect of stress frequency on surface crack propagation may be explained by the equivalent elasto/visco-plastic strain range at crack front based on the visco-plasticity of the materials.
This paper deals with the cumulative inelastic deformation (cyclic creep deformation) under cyclic loading. From the viewpoint of practical use, an attempt was made to evaluate the cyclic creep deformation by the finite element method based on the conventional creep analysis. In order to examine the fundamental properties of the cyclic deformation of a Fe-based cast heat-resistant alloy (XF818), the basic tests were carried out at various temperatures (500, 600, 700°C) and stress range lebels (113, 226, 339MPa) under the uniaxial load condition of constant stress ratio (R=0). By using the test results, the behavior of cyclic creep deformation of the material was expressed by an equation including the stress range, temperature and number of cycles so as to apply to the numerical analysis for estimation of the cyclic creep deformation. In the analysis, the conventional finite element creep analysis was employed by use of the time hardening deformation rule, replacing the elapsed time with the number of cycles. The finite element analyses and cyclic creep tests was carried out for two kinds of specimens in the conditions of temperature and stress distributions. From the comparison between the analytical and experimental results, the applicability of the proposed method was confirmed.
To investigate the temperature and strain-rate dependence of flow stress and strain-hardening behaviour of austenitic stainless steel (SUS304), tension tests and creep tests were carried out in the temperature range between 750 and 1200°C under the strain-rate from 1.0×10-5 to 1.0×10-2 S-1. Some typical inelastic constitutive equations, such as the types of Perzyna and Bodner as well as the superposition model, relevant to describe the high temperature behaviour were used to simulate the test results. The material parameters of these equations were identified to simulate cyclic stress/strain hysteresis. The model of Perzyna was found to be most adequate for the simulation of material behaviour up to 1200°C.
The aim of this paper was to study the applicability of a unified estimation method for evaluating strength of silicon impregnated silicon carbide. For this purpose, various kinds of bending tests, such as fast fracture tests, cyclic fatigue tests and creep fatigue tests, were carried out. The testing temperature conditions were 1100°C, 1200°C and 1300°C in atmosphere. Other temperature conditions of room temperature, 1000°C and 1350°C in atmosphere were added only in fast bending tests. The strength date obtained were analyzed by use of a unified estimation method. The results obtained are as follows: (1) The unified estimation method can be applied to the strength evaluation of silicon impregnated silicon carbide at 1100°C, 1200°C and 1300°C. (2) The temperature dependence of bending strength was different below and above 1300°C. Above 1300°C, the bending strength decreased with increasing temperature. (3) Crack growth rate index of silicon impregnated silicon carbide was obviously larger than that of silicon nitride from 1100°C to 1300°C.
In order to clarify the crack propagation behavior in the transition state from microstructurally small cracks to mechanically large cracks under creep-fatigue conditions, crack propagation tests were carried out using three kinds of specimens of a Type 304 stainless steel; (1) smooth specimens, (2) smooth specimens with small pre-cracks (about 100μm) introduced by fatigue at room temperature, and (3) through notched specimens. It was found that the scatter in the propagation rate due to microstructural inhomogeneity was emphasized for small cracks of shorter than 100μm in half length being equal to two grain diameters. Most of small cracks arrested and the maximum value of their propagation rates showed little dependence on the crack length. On the other hand, this scatter converged upon the mechanically large crack propagation rate when the half crack length on the specimen surface reached about 500μm. Numerical simulation was carried out based on a model of random fracture resistance of grain boundaries which had been used only for the simulation of small cracks. The model was also applicable to the transition state from microstructurally small cracks to mechanically large cracks.
The stress corrosion cracking or hydrogen embrittlement is defined as the localized fracture phenomenon caused by the interaction between applied stress and electrochemical process. Recently, a number of studies incorporating the electrochemical method and the slow strain rate technique (SSRT) have been carried out in various corrosive environments as a way for understanding the corrosion behavior of metallic materials in a short period. In this study, in order to clarify the corrosion behavior of two types of ferritic stainless steels which were made by laboratory, the SSRT tests were carried out under those potentials corresponding to the hydrogen evolution region, stable passive state region, transpassive state region and pitting corrosion region of the anodic polarization curve which was obtained in 3% NaCl solution. Also the changes of current and mechanical properties in both test specimens were compared and examined. The main results obtained are summarized as follows. (1) The presence of the stable passive and unstable transpassive state regions was confirmed in both test specimens from the measurement of anodic polarization curves in 3% NaCl solution. The passive film formed on No.2 specimen which contains 2% nickel may be considered as stable, because the passive current in the passive state region was constant. (2) From the change in current through the loaded specimen under various characteristic potentials, particularly in the case of the fixed potential of -0.375V (vs. S.C.E.) corresponding to the passive state region, the metal dissolution hardly occurs because the repassivation of passive film takes place rapidly even if it is ruptured by tensile deformation.
Stress corrosion tests were conducted by using SNCM439 steel in 3.5% NaCl solution under various cathodic potentials. The crack profiles obtained in these tests were analyzed by fractal geometry. The results obtained were summarized as follows: (1) The more base the cathodic potential is, the slower the crack growth rate becomes and the larger the branching width becomes. (2) The profile of main cracks under cathodic polarization has the fractal character. The fractal dimension measured by the yardstick method is of no significance to the stress intensity factor and polarized electrode potential. (3) The fractal character of stress corrosion crack branching under cathodic polarization measured by the box counting method shows the single region for the case of only micro branching, and it shows the double regions for the case of mixture of micro and macro branching.
“Hardness” and “ductility” of brittel materials are addressed on the basis of energy principle for their surface deformation processes. Details of the hysteresis behavior associated with Vickers indentation loading-unloading process are studied. The hysteresis loop energy is related to the plastic/elastic deformation, hardness, and the ductility of brittle materials where a novel parameter, work-of-indentation, ΓI (J/m3), is defined and experimentally characterized as irreversible energy dissipation for the formation of unit indentation impression. The ΓI reduces to the hardness, H, for perfect plastic materials. The finite difference between ΓI, and H of brittle materials arises from the elastic recovery of surface deformation after indentation unloading. The physical meaning of the hardness of brittle meterials is scrutinized.
In this paper, acoustoelastic laws for shear waves are theoretically investigated. First, the acoustoelastic effect in an isotropic material is analyzed in arbitrary propagation direction. From this, a generalized acoustoelastic law is formulated in terms of the secondary principal stresses. Confining to the acoustic birefringence, this relation becomes quite similar to the general photoelastic law. Secondly, a principal plane of a slightly orthotropic material is assumed to be coincident with a principal stress plane, and the acoustoelastic law for two polarized shear waves propagating in this plane is considered. As a result, it is shown that this relation is a linear combination of the stress effect given by the generalized acoustoelastic law for an isotropic material and the texture effect in a stressfree orthotropic material. Then, based on this, two important acoustoelastic laws for off-axis and grazing SH waves are rederived. Moreover, it is also confirmed that these relations are valid to within the second-degree of the texture effect. Finally, the acoustoelastic law for two polarized SH waves is modified to include the second-degree terms of the texture effect, from which it is confirmed that this modification does not affect the relation about the acoustic birefringence.