The addition of alloy elements such as silicon, chromium and molybdenum is effective in the restraint of temper softening in martensitic steels. The martensitic steel containing such alloy elements is known to have excellent resistance to temper softening in low and high temperature tempering treatments. However, the effects of the compound addition and its mechanism have not yet been satisfactorily revealed. In this study, the effect silicon, chromium, and molybdenum on resistance to the temper softening of the medium-carbon martensitic steel was investigated. As a result, it is revealed that the temper softening resistance quantity is maximum at the tempering temperature 773 K in the martensitic steel containing silicon, chromium, and molybdenum; this is because of the miniaturization of cementite (θ) and clustering of (Cr,Mo,Mn) 2C. Moreover, it is revealed to form this cluster at a tempering temperature lower than the temperature at which the alloy carbide usually precipitates (823 K-873 K).
In order to investigate in-plane anisotropy of cold rolled stainless steel strip for springs (JIS SUS304CSP-H), tension and compression tests were performed using a universal testing machine and for the latter test, a modified compression test method was applied. Uniaxial tension and compression tests on as received and low temperature annealed (400 °C, 1.5 h) samples were carried out in rolling direction (RD), 45°(DD) and 90°(TD) inclined to it were subjected respectively. It was observed that the tensile elastic limit (0.05% proof stress) and 0.2% proof stress were distinctly larger than the compressive proof stresses in RD, while in TD samples, these two kinds of tensile proof stresses were smaller than the compressive proof stresses. These relations in as received samples were kept qualitatively even after low temperature annealing although the proof stress differences became smaller compared with as-rolled ones. The proof stresses of the annealed samples were relatively higher than that of the as received samples. Thus, it was experimentally confirmed that the low temperature annealing decreased the anisotropy of as-rolled strip.
We measured the temporal change of residual displacement immediately after unloading at room temperature for three compression coil springs, SWP-B, DASH and SWOSC-V, with different Si compositions. All the total residual displacement of the compression coil spring changed logarithmically with time, and the total residual displacement increased with the compression holding time. Also, in the pearlite steel springs, the larger the Si composition, the smaller the total residual displacement. However, high-silicon oil-tempered steel spring, SWOSC-V, showed some increase of the total residual displacement. Furthermore, the total residual displacement became smaller under the magnetic field. These results suggest that the magnetic domain wall may be involved in the pinning of dislocations in the residual displacement.
It has been reported that the fatigue limit of shot peened high strength steels with a semicircular slit of 0.2mm or less in depth was improved to the same value as that of defect-free shot peened specimens. In this study ultrasonic shot peening (UP) which can introduce deeper compressive residual stress was noticed in order to investigate the effect of the depth of compressive residual stress on the size of surface defect that can be rendered harmless by peening. After UP was applied to the specimens of spring steel (SUP9A) with semicircular slits of 0.2, 0.3 and 0.4mm in depth, plane bending fatigue tests were carried out under the condition of stress ratio R=0.As the result, it was clarified that the defect size that can be rendered harmless by UP was at least 0.4mm. In other words, it was found that increasing the depth of compressive residual stress is effective in increasing the size of defect that can be rendered harmless. In addition, the predicted size of the defect rendered harmless by UP based on the stress intensity factor was consistent with the experimental results.
Effects of small surface defect on bending fatigue limit of spring steel (JIS-SUP9A) was investigated. Bending fatigue tests were carried out under stress ratio of R = -2, -1, 0 and 0.4 for smooth specimens and specimens having a semi-circular surface slit with the depth of 30, 60 and 400 μm. The fatigue test results revealed that the maximum defect size which does not affect the fatigue limit shows stress ratio dependency. Further, the prediction of fatigue limit of smooth specimen and threshold stress intensity factor range at arbitrary stress ratio became practical. Fatigue limits of the specimens having a slit with depths between 30 μm and 400μm were in good agreement with the values predicted by the new fatigue limit prediction equation.
In the previous report, the authors focused on the plastic behavior of fatigue crack tip and proposed a new equation of threshold stress intensity factor range for fatigue crack propagation including the stress ratio (R). The equation showed high accuracy on the fatigue limit prediction of high-strength steel with micro cracks regardless of the R. Using the equation, the following peculiar fatigue fracture behaviors of the shot peened materials were analyzed and discussed. (1) The maximum surface crack size that can be rendered harmless by shot peening, (2) The fatigue limit of cracked materials that cannot be rendered harmless, (3) The reason why most of the fracture origins of peened materials with harmless pre-crack are outside the pre-crack, (4) The reason why non-propagating cracks of stage II occur in most of peened materials. As a result, (1)-(3) was evaluated quantitatively, whereas (4) was evaluated qualitatively using the microscopic residual stress distribution after shot peening.
A measurement method is established to determine the elastic modulus of slender, flexible beams when they are subjected to the large deflections. Specifically, the deflections of cantilever beam and simply supported beam is used to determine the modulus of elasticity, Young's modulus. Present method is based on approximate formulas for the nonlinear relation between deflection and load under large deflection. By using the approximate formulas, we can easily obtain the dimensionless load parameters corresponding to the deflection without employing elliptical functions. The approach is validated with experiments using a steel piano wire. While this approximation formulas are easy to use and simple, it has high-precise approximation to the exact solution, consisting from elliptic integrals. Present method is also applicable to flexible thin plates and extremely delicate materials in order to obtain a quick estimate of the material's elastic modulus.
This paper describes a method for evaluating Young's modulus and the coefficient of friction between a beam and supporting member by three-point bending test in large deflection mode. The result of measurement, i.e., deflection-load curves, are employed for identifying both the elastic modulus of beam and the coefficient of friction. The large deflection three-point bending test with frictional force being considered is first analyzed on the basis of the large deflection theory of beam. Then, analytical results which consist of elliptical integrals, are represented by approximated polynomials in order to reduce the calculation cost in the identifying process. Next, an inverse procedure for determining the Young's modulus and the coefficient of friction is described by minimizing the evaluating function which includes unknown parameters. The approach is validated with experimental data using a piece of piano wire and an acrylic square bar. It is found that the present results showed good agreement with the values which are already known from the other experimental studies.
This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscously damped primary system. A series-type double-mass DVA was optimized using three optimization criteria (the H∞ optimization, H2 optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H2 optimization and stability maximization criteria. Because all actual vibration systems involve damping, the proposed expressions are expected to be useful in the design of DVAs. Furthermore, it is an important finding that the exact algebraic solutions exist even for such complex optimization problems of a linear vibration system.
In the optimization of dynamic vibration absorbers (DVAs), it is generally assumed that the damping force changes in proportion to the velocity of the object; this damping is called viscous damping. However, many DVAs used in practical applications are made of polymeric rubber materials having both restorative and damping effects. This polymer material is considered to show a hysteretic damping force that is proportional to the displacement rather than the velocity of the object. Despite the widespread use of such hysteretically damped DVAs, there are very few studies on their optimal design, and yet the design formula of the well-known general viscously damped DVA is presently used for the design of this type of DVA. This article reports the optimal solution of this hysteretically damped DVA. For generality, it is assumed that the primary system also has structural damping that can be treated as hysteretic damping. Two optimization criteria, namely the H∞ optimization and stability maximization criteria, were adopted for the optimization of the DVA. For these optimization criteria, exact algebraic solutions were successfully derived.
There is not sufficient analysis for practical problems such as large deformation of a medical guide wire (catheter) in a blood vessel, or of a cable in a channel (or a pipe), of a drill inserted in a drilling hole in rock engineering and petroleum production, and so on. When a thin flexible beam is pushed through the narrow space, the beam may buckle since the leading edge strikes an obstacle (or a barrier) and cannot proceed any more. The large deformation behavior will be of great concern in handling these flexible materials.
This paper deals with large deformations of a flexible elastic beam contained in a rigid body with friction under the action of axial compressive forces at each fixed-supported end. Three different deformation stages in a rigid body are prescribed for our analysis. Using the nonlinear deformation theory, nondimensionalized analytical solutions are derived in terms of elliptic integrals. In this study, several experiments were presented and the experimental results were compared with the theoretical formulas.
As a result, the relation between the applied axial force and the horizontal distance is similar to that of predicted calculation by the analytical theory. Furthermore, it is made clear that the existence of friction between the beam and the rigid wall causes a nonuniform large deformation. Incidentally, the analysis presented in this paper would be applied to the medical guide wire (catheter) and the design of machinery for handling flexible elastic materials such as sheets, tapes, films, papers, cloths and so on. In addition, designers of machines for drill, tubing strings, sewing machines should find the results useful and easy to apply.
In this study, 3D finite element analyses have been made on the stress intensity factors for semi-elliptic surface cracks in tension coil springs of generally anisotropic materials in order to investigate the effects of elastic anisotropy on the correction factors, Fi (i = I, II and III) for the three modes of the stress intensity factors. The generally anisotropic stiffness matrix was determined by changing the off-diagonal components Cij (i ≠ j), except C12, C13, C23, of the stiffness matrix modelled by a ferrous material. When the values of the off-diagonal components are changed simultaneously, the maximum value of the correction factors for all the three modes increased sharply as these components approaches to the values of one of Lamé's constants, or the shear modulus, G. The value of FI, the correction factor for the mode I stress intensity factor takes local maxima in the vicinity of surface, i.e., ϕ = 0°∼90°and 150°∼180°, the FII value at surface, i.e., ϕ = 0°and 180°, and the FIII value at ϕ = 45°and 135° where ϕ is the eccentric angle of the semi-elliptic crack. When only one of the off-diagonal components Cij is set for near the G value and the others are 0, the variations of the correction factors with the value of ϕ are revealed to be similar to those for the case where all the values of the off-diagonal components are set for near the G value. These results imply that the correction factors for the mode I to III stress intensity factors of semi-elliptic surface cracks in generally anisotropic tension springs can be largely affected by the values of the off-diagonal components C45 and C46 of the stiffness matrix of the spring wire.
This study has made 3D finite element analyses on the stress intensity factors for semi-elliptic surface cracks in compression coil springs of cylindrically anisotropic and orthotropic materials in order to clarify the effects of the anisotropies on the correction factors Fi (i = I, II and III) for the three modes of the stress intensity factors. The cylindrical anisotropy was modeled by the stiffness tensor composed of the same components as those of the orthotropic material plus the additional C45 component. In the cylindrically anisotropic coil springs, the mode-I correction factor FI was dominant being the order of 0.7-0.9 around the periphery of the cracks. As the C45 value increased, the FI value decreased around the periphery of the cracks except for the vicinity of the wire surface. The absolute values of FII and FIII, however, increased locally beyond 1. In the orthotropic coil springs, FI was also dominant being the order of 0.9. The absolute values of the other correction factors remained less than 0.2 and reached the highest value in the vicinity of the wire surface. Not only the values but also the distributions of the three kinds of correction factors around the crack periphery in the orthotropic coil springs were found not so different from those of the semi-elliptic surface cracks in the isotropic compression coil springs.
Though there are many activities to define delayed fracture method by professors, professional engineer and any specialists, there is still no standardized delayed fracture test method, and Automotive OEMs have their own ideas and test methods for reasons of the above. Considering background of the recent high hardness spring design, we need to prepare standardized test method to prevent delayed fracture risk in the future. Therefore, the research committee have been in action to standardize delayed fracture test method simulated automotive environment. The issues to be solved are as bellows, First issue is to establish hydrogen analysis method to separate hydrogen occurred in the rust remained on material surface.
Second issue is to estimate maximum hydrogen content entered from automotive environment.
Third issue is to confirm an evaluation method to occur delayed fracture by grasping the coil spring simulated fracture pattern in the market.
4th issue is to establish an evaluation method used test piece to be reproduced fracture pattern in the market.
This study reports experiment results for the first and second issues as in September 2019.