A stochastic model for predicting the strength and reliability of unidirectional fiber-reinforced ceramic matrix composites is proposed, in order to find theoretically statistical properties in strength of the composites, composed of constituents with large variations in strength. In the proposed model, mechanical behaviors of the composites follows the Curtin's assumptions, of which validity was examined by a FEM analysis. The proposed model is based on a Markov process, in which it is assumed that a damage state in the composite is developed with each fiber breakage. When the Weibull distribution is used as a strength distribution of the fiber, the probability of being in each state is analytically solved as a function of stress. The expected value and variance in the composite stress were then estimated from the probabilities of being in states. Furthermore, the maximum stress of the expected value, i.e. the strength, is predicted together with the coefficient of variation. The results showed that, even if broken fibers are imperfectly recovered in stress along the fiber-axis from the breakage points, the composite exhibits a higher strength and reliability than that of a dry bundle. Finally, it is concluded that stress recovery in broken fibers is a significant mechanism to determine the strength and reliability of the composites.
In this study, the tunneling algorithm is applied to the first order reliability method (FORM) to find a global design point. In the FORM, the structural reliability is evaluated as the minimum distance from the origin to the limit state surface in the standard normal distribution space. Therefore, the FORM is formulated as a nonlinear optimization problem. However, it is difficult to find the design point, when the limit state surface has several local minimum points such as a case of the laminated composite plate subject to the first ply failure. In general, the original tunneling method is not worked well for the constraint problem. In this study, a new tunneling function suitable for the FORM is proposed to find the other design point which has a lower objective function value and satisfies the equality constraint. In the tunneling function, the limit state function is treated as a kind of a penalty term with a pole. Through the reliability analysis of a laminated composite plate subject to in-plane loads, the efficiency of the proposed tunneling function is demonstrated. Also, the selection of the penalty parameter is suggested.
The ceramics/metal joints in the airtight seal parts for a neutron detector are studied on the reliability for strength and long-term life. Both functions of airtight and insulation are required for the airtight seal parts, which suffer a very bad influence from a viewpoint of long-term reliability as well as strength, because the residual stress is generated in these joints due to the difference of the thermal expansion coefficient between ceramics and metal. The ceramics subjected to neutron irradiation in-serve occurs in swelling (volume expansion) and decreases in strength. Moreover, the copper interlayer rises in yield stress and hardens with increasing the plastic deformation due to the swelling of ceramics, and so lowers in function for stress relaxation. As a result, not only the internal stress in ceramics increases with passing the time in service, but also the facture strength of ceramics lowers, and finally a delayed fracture occurs at the ceramic/metal joints in the airtight seal parts. Therefore, in our study, the residual stress has been analyzed by a simulation model using FEM, so that both mechanisms of the increment in internal stress as well as mechanical damage can be clarified for the ceramic/metal jointing parts subjected to the neutron irradiation over long-term. On the other hand, the strength verification against the ceramic/metal joints are performed through simulation model analyses as well as the virtual tensile tests for small mock up specimens. From a viewpoint of fracture mechanics, the reliability for fracture life as well as strength of the airtight seal parts is discussed statistically considering the scatter of strength for Si3N4.
Residual stress generated by thermal expansion coefficient mismatch between ceramic and metal is an important problem affecting the strength of ceramic-metal joints. An interlayer, which is a ductile metal, is often inserted between ceramic and metal in order to relax this residual stress. In this study, the residual stress produced in the joint-cooling process is analyzed and 4-point bending tests are carried out. From the viewpoint of experimental observations and fracture mechanics, the effects of interlayer thickness on joint strength in ceramic/metal joints are discussed considering the superimposed stress distribution of the residual stress and the bending stress. Joint strength is then estimated based on fracture mechanics and fracture probability considering the superimposed stress, crack size and position of pre-existing defects in the ceramics. The optimum interlayer thickness for the present specimen is identified, and the estimation method is extended to the analysis of generic joint strength using normalized strength of ceramic by expressing joint strength in terms of normalized strength considering the scatter of joint strength and the effective volume.
Static and cyclic fatigue strength in porous SiC and Cordierite ceramics were evaluated using quasi-static and cyclic tests, i.e. applied force, P, increasing and applied force range, ΔP, increasing tests, respectively. The evaluation method used Weibull distribution, in which the fracture parameters are stress at failure, σf, for quasi-static loading and maximum stress at failure, σmax, f, for cyclic loading. The results revealed that the static fatigue behavior had an important role on the degradation of fracture strength and that cyclic component of loading do not influence on the fracture strength. Statistical characteristics of the fatigue strength were expressed by P-S-N curve estimated by the results of ΔP-increasing tests. During the fatigue experiments, crack nucleation was detected using acoustic emission (AE), and the fracture surfaces were observed by SEM. Based on these results, fracture mechanisms of the porous SiC and Cordierite ceramics were controlled by particle binders, and the binder fractures have a great variety of magnitude.
Diaphragms made of stainless steel plates are widely used as switching parts in electrical devices. Since the cyclic loading is applied to these diaphragms by the repeated switching mode of on/off, the estimation of the fatigue life of diaphragms is very important. The fatigue characteristics of the diaphragm must be discussed considering the large scatter of material properties induced by the anisotropy. In this study, the tensile and the fatigue tests have been carried out for some specimens with a direction to cold rolling direction. A pulley driving system has been adopted as a fatigue testing apparatus because the load can be applied even when the thickness of the specimen is less than 0.1mm. From the experiment, it is recognized that the experimental data is scattered largely. In addition, the residual stress is generated by a press forming process and the stress acts on the diaphragm as a mean stress. In order to estimate the reliability of a diaphragm, therefore, the Goodman diagram with a design margin which can be considered the mean stress for fatigue can be obtained. We have proposed the method which can evaluate the reliability of a diaphragm to design life by Goodman diagram.
Fatigue characteristics of a metal diaphragm in a light touch switch are evaluated with experimental approach considering cyclic load acting on it. The approach consumes much time and costs for evaluation. In previous paper, we have described that the mechanical properties of stainless steel have anisotropy and the fatigue characteristics must be discussed considering the large scatter of material properties induced by the anisotropy. Therefore, the purpose of this study is to establish a simple method to evaluate the reliability of diaphragms with the consideration of anisotropy. The proposed approach consists of three procedures. Firstly, residual stress after press forming is evaluated by finite element method (FEM), and response curves when the pushing load is applied on the diaphragm are also analyzed. And, the stress amplitude and the mean stress at every point on the diaphragm can be calculated. Secondly, the experimental database about S-N curve and Goodman diagram considering the effect of anisotropy have been prepared. Finally, the fatigue lives considering failure probabilities on the diaphragm can be estimated by comparison of Goodman diagram with numerical results. Obtained results revealed that the proposed approach is very useful for the reliability evaluation of the diaphragm.
A methodology is presented for performing probabilistic life assessment for individual parts based on statistical damage analysis and stochastic damage simulation analysis of actual turbine components. Examples are shown for thermomechanical fatigue (TMF) damage of gas turbine nozzles and steam pipes. TMF damage is multiple cracking and damage parameters are maximum crack length and crack length density. Applying the experimental damage parameters vs. cycle ratio relationships to the field crack data of individual parts, specific crack growth trend curves are derived as well as parts service conditions such as plastic strainrange. Using parts service conditions and stochastic damage evolution law of materials, Monte-Carlo damage simulation analysis is performed. The simulation analysis is the useful tool for the probabilistic life prediction for individual parts and for risk-based maintenance and repair/replace judgement.
It has passed one century since French G. Charpy proposed the Charpy impact test in 1901. Instrumented impact test recording load history during fracture has been attempted since 1920's. It has become possible to obtain various information from this method. However, succeeding development of fracture mechanics has made it also as a qualitative screening test. To obtain quantitative fracture toughness parameters from this method, therefore, has been desired eagerly. The author developed successfully a computer aided dynamic fracture toughness evaluation system, called CAI system already in 1980's. This paper reviews development and progress in the Charpy test, especially focusing on problems of evaluation of dynamic fracture toughness by the instrumented impact test and on accuracy of measurement in the test.
We investigated the damage characteristics in carbon fiber reinforced plastics (CFRP) laminates impacted by soft body and hard body projectiles launched by an air gun. Three kinds of silicone rubber were used as soft body projectiles to investigate the damage resulting from soft body impact that includes material non-linearity and large deformation. Plastic and metallic materials were used as hard body projectiles. From the C-scan images obtained with a scanning acoustic microscope after the tests, we found that the damage mechanism of CFRP laminates in the soft body and hard body impacts was the same. The maximum impact force for each projectile was computed based on the energy balance model and the fundamental hydrodynamics. From this analysis, we found that there is a critical impact force for the delamination initiation and that it is independent of the material properties of the projectiles.
Friction welding of 6061 aluminum alloy was carried out in order to examine the relationship among deformation heat input at the upset stage, upset burn-off length and joint performance. The joint performance was evaluated by tensile testing and fatigue testing. Stabilized tensile strength was obtained when the deformation heat input at the upset stage and the upset burn-off length exceeded 200J/s and 4mm, respectively. Weld condition at the weld interface and the width of softened area affected fatigue strength more than tensile strength. That is, when the weld condition at the weld interface is good and the softened area is wide, fatigue strength increases because the stress disperses in the softened area. On the other hand, when the weld condition at the weld interface is good and the softened area is narrow, and when the weld condition at the weld interface is somewhat poor in spite of the wide softened area, fatigue strength decreases because the stress concentrates at the weld interface. The fatigue limit obtained by the fatigue testing reveals that, when the deformation heat input at the upset stage and the upset burn-off length exceed a certain value, sound joints can be produced.