Fractography is an experimental technique often used in failure analyses or investigations aimed at improving fracture property. Because fractographic features are controlled by the underlying microstructure, for a better understanding of fractograph it is neccessary to have correlations between fractographic and microstructural features. A variety of methods have been applied to obtain these correlations, including the following: (1) direct etching of the fracture surface to reveal the underlying microstructure; (2) simultaneous observation of the fracture surface and the corresponding section after the removal of the electrolytical material; (3) combined observations of the fracture surface and the section. In this note the three methods mentioned above are discussed, being applied to impact fracture surfaces. The main results obtained are summarized as follows: (1) The method of the combined observations gives us most correct and precise knowledge of the fracture. (2) The method of the simultaneous observation has two drawbacks: the removal of the electrolytical material may damage the fracture surface and the fragment of the electrolytical material may be left on the fracture surface. (3) The grain boudary is not recognized by the method of direct etching.
The dynamic response of a composite beam laminated by different materials may differ from the beam of one material. The purpose of the present investigation was to discuss the strain behavior of laminated composite beams under impact load and to compare the experimental results with theoretical ones. The problem considered here was the initial process of axial strain due to a lateral impact to the beam of three or five layers; it had steel layers together with one acryl resin layer at the middle, or two acryl layers with one middle steel layer. The dynamic flexural strains in certain cross sections of the beam were measured, and the strains corresponding to the measured positions were calculated, by the classical and Timoshenko beam theories as well as the finite strip method. The following was revealed from the results: (1) Just under the point of impact, the bending strain in the upper layer was larger than that expected from the normal distribution of strain in the cross section in the initial period of about 400-600 microseconds, and it changed to that of a natural vibration of a beam after the duration time of about 1 millisecond. (2) The finite strip method was valid to describe the behavior in all duration times, but the classical and Timoshenko beam theories agreed only after moving to natural vibration.
An annealed mild steel bar (250mm in length, 14mm in dia.) was subjected to compressive impact at various velocities. The experimental results showed that the mild steel possessed particular deformation behaviors such as a delayed yielding phenomenon and an appearance of local residual strain in the neighborhood of the impact end. In addition the analysis of dynamic behavior of the mild steel was made by using a Malvern-type constitutive equation proposed by the authors. From the comparison of the numerical results with the experimental results, it became clear that the experimental phenomena were explainable by the present analysis which takes into account a high strain rate sensitivity for the yield point. It was also found that the effect of strain-rate dependence on the deformation behavior of the bar was large.
Stress wave induced by the longitudinal collision of an elasto-plastic bar with either a rigid wall or an elastic bar was analysed numerically. The constitutive equation of the elasto-plastic bar was assumed to be rate-independent. A steep rise in axial stress at the impact end occurred immediately after collision and the peak value of the average axial stress within the cross section of the impact end was found to be equal to the predicted value as calculated using the stress-strain relationship in a uni-axial strain state. This is because, during a short period after impact, the immediate area of the impact end is in a state of uni-axial strain caused by its radial inertia. This high stress level dropped and relaxed as the dilatational wave propagated from the cylindrical surface to the central axis. This stress rise was apparent only in the space equivalent to one measurement of the bar's diameter. Beyond that point there was no particular rise in stress. The stress level oscillated and asymptotically approached to a constant value, which is calculated by Karman's theory in a uni-axial stress state.
In studying the dynamic behavior of a body under impulsive loading, it may be fundamentally important to analyze elastic/plastic deformation at a contact part and to analyze the impulsive force generated at that part. So, in this study, the deformation at the contact part and the generated impulsive force were measured through the experiments in which aluminum bars collided axially, perpendicularly against the impact surface of a sensing plate which had been devised by one of the authors. The aluminum bars used had contact ends in the shape of the circular cone or truncated cone (frustum). The impact velocity of the bars was varied from 0 to about 11m/s. It was found through the experiments that a new truncated cone was formed at the contact end, and that the conical angle of the cone depended only on the conical angle of the former cone before the collision. It was also confirmed that the generated mean stress of the boundary plane between the deformed part and the undeformed part at the impact end was constant independently of the shape of the cone and of the impact velocity. A simple and practical formula was derived with which the impact force generated at the contact part can be estimated for the collision of a body having a convex surface against a rigid wall, and a good agreement with the experimetnal results was obtained.
A constitutive equation dependent on the strain rate was proposed and was applied to carbon steels. It was derived from the approximation of two different dislocation movements, that is, one being dominant at low strain rates and the other at high strain rates. Compressive tests for four carbon steels (0.19%C, 0.37%C, 0.45%C and 0.57%C) were conducted under various constant strain rates ranging from 10-4 to 1000/sec by using three types of testing machine. Stepped strain-rate tests were also conducted to obtain the correction factor of the strain rate hysteresis effect on the stress-strain relation. The present constitutive equation was applied to the measured stress-strain relations. As a result, it agreed well with the experimental values. The experimental constants included in the equation were found to be determinable from a comparatively small number of experiments. So, the present constitutive equation seems to be valid for practical use.
The study of wave propagation in the machine-structures with varying cross-sectional parts has become very important from the view point of the impact strength of structures. In the present paper, first, the stress wave propagation and the impact fracture of a conical bar were treated experimentally. The changes of the crack location and the number of fracture points were investigated at several different impact velocities. Next the wave propagation in a conical bar was calculated by the finite element method, and its change with time was considered in detail. Furthermore the estimation of a crack location was tried. The results obtianed are as follows: (1) The wave speed, obtained from the experiment of the wave propagation in the conical bar, agreed with that of the one-dimensional theory. (2) When the impact velocity increased, the number of fracture points increased and the crack location approached to the top end of the conical bar. (3) The wave front of compressive strain was reflected at the top end as the tensile strain. These reflected tensile waves were superposed to the following tensile wave, and high tensile stress appeared often as observed in the experiment. (4) The crack location simulated in a conical bar of gypsum agreed fairly well with the experimental result.
The electrohydraulic forming method makes use of energy generated by impulsive high current discharge across electrodes which are usually bridged by an initiating wire. In this investigation, the wave forms of this discharging current and discharging voltage across electrodes were measured under various spark conditions. The electrical characteristics of the spark gap and the behaviour of exploding wires were made clear based on the wave forms obtained. In the wave forms of current and voltage, discontinuity points appeared as the phase of exploding wire changed from a solid state to a liquid phase and to a vaper phase. The time when the discontinuity points appeared was closely affected by the spark conditions. The value and the profile of the pressure wave generated by an exploding wire across the spark channel in water were calculated theoretically. These results were in good agreement with the experiments and could explain the characteristics of the pressure wave.
It is very important industrially to estimate the degree of large deflection appearing in such members as a plate spring, plastics and so on. In this report, the problem of large deflection of a simply supported beam in a symmetrical three-point bending test was treated. It was shown that the desired specific quantities such as maximum deflection, maximum curvature, maximum bending stress and end slope, which are especially matters of great concern in the material testing, were able to be predicted easily from a conventional linear bending theory and two reduction factors derived here newly. For the convenience of applications, the nomographs of the reduction factors were described graphically in terms of the vertical load, the large deflection at midpoint and the end slope. An experimental investigation of large deflection of a PVC thin plate was performed to confirm the availability of the newly proposed reduction method. The experimental results obtained were in good agreement with the predicted ones by the reduction method. Therefore, the simple reduction method can be put into practical use.
Rate type constitutive equations of elastic/viscoplastic materials are proposed. The constitutive equations have been obtained by introducing an excess stress term into Tokuoka's constitutive equations of elastic/plastic materials based on hypoelasticity. His equations have two kinds of internal variables (hardening parameters), and they have been proved to describe characteristic properties of elastic/plastic materials, e.g., yielding, unloading, reloading, flow rules, isotropic hardening, Bauschinger effect etc. The proposed constitutive equations reduce to Tokuoka's ones for sufficiently slow deformations, and they can also exhibit several strain rate effects. That is, they can describe rate sensitivity of the yield surface, the stress response for sudden change of the strain rate, creep, relaxation etc. An explicit form of the constitutive equations of von Mises type elastic/viscoplastic materials has been derived from general constitutive equations, by use of the representaion theorem for tensors, symmetry of tension and compression, the principle of material frame indifference etc. As an example, the above strain rate effects in uniaxial tension are analyzed, and significant agreement with the experimental results is shown.
The influence of strain rate and temperature on the flow stress of nickel chromium molybdenum steel (SNCM 439) was studied through experiments. In the experiments, thin walled tubular specimens of short gage length were loaded at strain rates of 70-103sec-1 in shear by using a torsional split Hopkinson bar apparatus, and loaded at strain rates of 10-4-10-1sec-1 by using a combined tension-torsion loading apparatus and an Instron testing machine. The experiments were performed in shear over the temperature range -185°C to 120°C. It is shown that the strain rate sensitivity of the yield point and of the flow stress in the region of small strain at -185°C and -60°C is remarkable, and that, below about -50°C, the influence of temperature on the flow stress reveal itself remarkably. It is confirmed that the experimental results obtained on the strain rate dependency and the temperature effect on the flow stress can be described fairly well with the practical constitutive equation for an elastic/viscoplastic body proposed by one of the authors. The values of the parameters contained in the constitutive equation are also presented.
A mechanism of delayed fracture under static load was proposed for fine grained nuclear grade isotropic graphite. Rectangular specimens were loaded in 3-point bending mode to the neighbourhood of the fracture stress and kept at about the same stress level by using an Instron type testing machine. The discrete acoustic emission (AE) signals were generated before the specimen completely fractured. This fact indicates that microcracks are produced or propagate discontinuously within the specimen under static load. This phenomenon was explained by a model in which the microstructure of graphite is regarded as the combination of elastic and plastic parts. According to the model, the stress relaxation in the plastic part induces an increase in stress at the region of crack tips or some kinds of defects in the elastic part.
In the previous paper, the authors' method for breaking high carbon steel rod into billets was introduced, in which a cross-sectional crack was developed from a slight sharp peripheral notch of the rod by rapid local heating and cooling. Furthermore, the hardness and residual stress distributions of unnotched specimens of high carbon chromium steel (SUJ 2) were measured after they were subjected to local treatment under various heating and cooling conditions including optimum ones for breaking notched rods. In the present study, the residual stress distribution in the notched section of SUJ 2 specimens caused by local rapid heating and cooling was evaluated by FEM calculations based on the assumption that the heat-treated state is substantially the same between the unnotched and notched specimens. First, the measured residual stress distribution in the unnotched specimen was reproduced in the unnotched FEM model in which local initial strain distribution was properly given. Secondly, the same local initial strain distribution was applied to the FEM model having a notch or crack extending from the notch root. The crack lengths developed in the actual rod breaking tests were discussed in relation to the residual stress distribution calculated using the notched FEM model as well as the mechanical properties of rods. The results obtained are as follows. (1) The distribution of axial residual stress measured in the unnotched specimen was satisfactorily reproduced by giving a reasonable local initial strain distribution to FEM model. (2) The calculated residual tensile stress in the axial direction near the notch root was relatively higher and more deeply distributed under conditions causing cracks than under those not causing cracks. (3) The breaking tests of SUJ 2 rods showed that cracks propagated to the depth where the calculated axial stress at 0.1mm depth from crack tip (σeff) comes down to a value nearly equal to the net breaking strength of the rods (σt).
The purpose of this paper was to investigate quantitatively the effect of transverse residual stress on fatigue crack propagation in the field of biaxial tensile residual stress, which exists in the normal and parallel directions to the crack surface, based on the experimental facts and the linear fracture mechanics. In the experiment, the X-ray oscillating stress measurement method was used to examine the residual stress distribution arround a precrack in the plate specimen which was made so as to have biaxial tensile residual stress due to water cooling from the temperature 873K. By using these specimens, it was confirmed that the crack propagation rate and the crack opening displacement CODmax were reduced by transverse tensile residual stress. On the other hand, it was found that the initial stress intensity factor of precrack in the biaxial residual stress field could be estimated from the measured value of longitudinal residual stress by using a linear fracture mechanics model. The effective stress intensity factor range calculated from both the initial stress intensity factor of precrack and the applied maximum stress intensity factor which was corrected so as to have the same CODmax between transverse and no residual stresses by using Dugdale model was useful to understand the fatigue crack propagation rate in the biaxial as well as the uniaxial longitudinal residual stress fields.
In order to reduce the weight of machine elements. Al-Si cast alloy (AC4A-T6) was examined to use it for the cover of crankcase instead of grey cast iron (FC25). The fatigue strength of AC4A-T6 and FC25 specimens taken from the cover of crankcase was determined by applying cyclic load prescribed from the local strain at the notch of specimens. The main results obtained were as follows. (1) The fatigue strength under the stress ratio R=-0.5 at N=107 of AC4A-T6 specimen was 68.6MPa, which is the same as that of FC25 being used presently for the cover of crankcase. Thus AC4A-T6 can be used for the cover of crankcase instead of FC25. (2) It was observed through fractography using SEM that the fracture surface of the crack initiation of AC4A-T6 consisted of small pores and crystal facts existing in matrix microstructure. Therefore, it is considered that porosity and matrix microstructure control the fatigue strength of AC4A-T6.
The cyclic fatigue behavior of sintered silicon nitride was investigated at room temperature. Flexure specimens, with an indentation induced flaw at the center of the reduced gage section, were tested, where the cyclic load was applied by four-point bending up to frequencies of 10Hz using an electrohydraulic testing machine. Sintered silicon nitride showed a susceptibility to cyclic fatigue, and its lifetime decreased with increasing maximum applied stress. An apparent fatigue limit was about 70% of the flexural strength. A couple of crack arrest position marks around the indentation were detected in the fracture surfaces of both flexure and fatigue test specimens, and the size of each mark well corresponded with the analytical result based on a contact residual stress. Frequency did not affect the lowest limit of the fatigue lifetime, although a scatter of the data and the highest limit of the life-time increased as the frequency was lowered from 10Hz to 0.01Hz. High magnification fractography revealed an intergranular dominant fatigue failure with partial transgranular failure at perpendicularly elongated crystals. It suggests that the intergranular fatigue crack can be arrested at grain boundary triplets, and also can be reactivated by subsequent cyclic loadings. The crack growth rate calculated from the fatigue lifetime showed a three region characteristics having a plateau at 70 to 90% of the fracture toughness, which suggests the possible intergranular stress corrosion cracking mechanism resembling that in glass or alumina.
Sakai etal. established the “correlation factor method” for estimating 3-parameters in Weibull distribution function. However, this method can only be applied to mono-modal fracture models. In this work, for analyzing multi-modal Weibull distribution function we suggested a new estimating method, namely the multi-correlation factor method, by employing Kaplan-Meier method which can separate the data into individual causes of fracture. By Monte Carlo simulation for bimodal Weibull distribution function (6-parameters) we compared the multi-correlation factor method with the multi-maximum likelihood method. It was concluded that the multi-maximum likelihood method was more accurate than the multi-correlation factor method. Further, we estimated six Weibull parameters for 403 data of Si3N4 obtained by 3-point bending tests.
The acousto-elastic effect was studied experimentally by analyzing the Fourier spectrum of ultrasonic waves. Uni-axial tensile stress was applied to several specimens made from rolled plates of aluminum, copper and steel, and ultrasonic transverse pulses were sent into these specimens with a PZT transducer, which was also used to detect reflected pulses. Since an incident transverse pulse was resolved into two constituents due to the slight orthotropy of a rolled plate and the application of stress, certain frequency components disappeared in the spectrum of a reflected resultant pulse. This frequency, called the zero-point frequency here, was measured with an analog-type spectrum analyzer, and its variation with the stress was examined. In the specimens with the loading direction parallel or perpendicular to the rolling direction, the experimental results showed that the reciprocal of the zero-point frequency varied linearly with the stress, and the acousto-elastic constant of each plate was determined from the slope of this linear variation. In the aluminum specimen whose loading direction was inclined by 45° against the rolling direction, it was shown that the polarization direction of transverse pulses rotated with the stress. These results agreed well with the acousto-elastic law for a slightly orthotropic material. It is concluded that the method of spectrum analysis is much suited for the measurement of acoustoelastic effect.
It is well known that in structural materials used for power and chemical plants, creep or fatigue damage accumulates during long-term use at high pressure and temperature due to the change in metallurgical structure. In the past, the life prediction of structural material used at high temperatures had been carried out through the destructive test data. Recently, however, there has been an attempt to utilize the data of various material properties measured by non-destructive testing methods. The purpose of the present investigation was to study the relation between creep damage and material properties measured non-destructively, such as electric resistance, hardness and sigma phase area. The material used in this study was solution heat treated 18Cr-8Ni (Type 304) austenitic stainless steel. The test specimens were subjected to the long-term heating and creep damage before testing. The preparatory conditions were: temperature of 750°C, loading period of 200-1500 hours and creep damage of 0.2-1.0. The creep damage was determined based on the time fraction rule, and the creep damage of 1.0 was defined as the normalized time when the test specimen was ruptured. The electric resistance, hardness and sigma phase area of the crept specimens were measured at room temperature. The results obtained are summarized as follows. (1) The ratio of electric resistiviy decreased with increasing creep damage in the range of small creep damage, and it became minimum at a certain value of creep damage. Then, the ratio of electric resistivity increased with increasing creep damage. (2) Vickers hardness increased with increasing creep damage. (3) The percentage of sigma phase area increased with increasing creep damage. These results suggest that the creep damage during long-term service in austenitic stainless steel can be detected by means of a non-destructive method, such as the measurement of electric resistance, hardness or sigma phase area, and that it is possible to estimate material life by such non-destructive testing method.