Saburo Usami

Strength of ceramic materials containing small flaws

Abstract Ceramic strength values for different flaw sizes, grain sizes and notch radii are analyzed with a grain-fracture model. The critical stress-intensity factor for small flaws is lower than that for large cracks. Therefore, conventional LEFM is not applicable for estimating ceramic component strength. However, the relationships between the ratio of equivalent crack length and mean grain diameter, a e d ,and the ratio of critical stress-intensity factors for short and long cracks, K c K Ic ,are almost identical for various kinds of ceramic materials. This fact is well expressed by the model. Moreover, both the effect of grain diameter on plain specimen strength and that of notch-root radius on the notch-toughness value are explained well with the model utilizing the KIc value of materials.

Cryogenic small-flaw strength and creep deformation of epoxy resins

Resin cracking, a cause of coil quenching in superconducting magnets, occurs when a resin contains small flaws and sustains high thermal stress. Seven epoxy resins were chosen in order to evaluate thermo-mechanical properties, small-flaw strength, and creep deformation at low temperatures. Although the plain specimen strengths consistently increase as the temperature decreases, the fracture toughness resulting from large cracks reaches a maximum at around 80 K and then decreases at 4 K. The loss factor during cyclic loading behaves similarly, because of low-temperature relaxation of the resin, and has a maximum value at around 150 K. The strengths resulting from decreasing flaw size level off to those of plain specimens; that is, they deviate from linear fracture mechanics. Thermal stress (caused by coil restraint) in the epoxy resin is experimentally measured by simulating the coil molding process. These thermal stresses are close to the calculated ones obtained by using the elastic moduli and the coefficients of thermal expansion of the resin. However, they are a little lower because of stress relaxation at around the glass transition temperature. Thermal stress and small-flaw strength at 4 K are used to calculate the critical volume-ratio of resin to conductor that produces coil quenching as well as the allowable flaw sizes. The calculated ratios and sizes of the resins vary considerably. Even at 77 K, creep deformation in the resins is significant and may cause a cryogenic delayed fracture of the resin and result in unexpected coil quenching during steady-state persistent-current operation. And the ratios of the creep strain to the initial strain (in all resins tested) decrease uniformly as the difference between glass transition temperature and test temperature increases.

Creep deformation of austenitic steels at medium and low temperatures

Abstract An austenitic steel used as a structural material of a superconducting magnet undergoes creep deformation and stress relaxation even at medium and low temperatures. Small plastic and creep strains in eight austenitic steels and a low-alloy steel were measured in the temperature range from 4 to 573 K. Every steel including the low-alloy steel showed logarithmic creep strain at these temperatures when stress was high enough to produce plastic strain. Although the creep strain rate in specimens, JIS SUS316L, at 293 K was proportional to about the 7th power of stress when the stress was around 0.2%-plastic-offset stress, the order of the power decreased to 1 as stress decreased. The ratio of creep strain at 105 s to plastic strain was in the range 1–3 at 293 K and 0.5–2 at 77 K, though the precipitate-hardened steel JIS SUH660 had a lower ratio. When creep strain at 105 s was 0.02% at 77 K, the stresses ranged 0.7–0.85 of 0.2%-plastic-offset stress. As creep strains were smaller than plastic strains at lower and higher temperatures, the ratios of 0.02%-creep-offset stress at 105 s creep to 0.02%-plastic-offset stress were as high as 1.5 both at 4 and 573 K. These ratios were lower (0.9–1.0) between 77 and 450 K. Creep deformation in a component can be prevented by pre-straining with a plastic pre-strain larger than the estimated inelastic (plastic plus creep) strain during operation. The pre-straining effect is also effective even when operation and pre-straining temperatures are different.

Static-fatigue limit of ceramic materials containing small flaws

Abstract The crack growth behaviors from flaws of different sizes in ceramic materials are observed under elevated-temperature static-fatigue loads. The cracks initially decrease and then increase the growth rates, resulting in specimen failure; or they are arrested after small extensions, resulting in the static-fatigue limit of the specimen. The threshold stress intensity factor at the static-fatigue limit is lower for small defects than that for large defects, i.e., the static-fatigue limit levels off for the small defect, as in the case of a brittle fracture. Also discussed are the effects of temperature, environment and material on the static-fatigue limit value. A proof test method for elevated-temperature ceramic components is proposed.

Thermo-mechanical properties of epoxy GFRPs used in superconducting magnet winding ☆

Abstract A tightly constructed rigid structure of a conductor winding and GFRP spacers in a coil case is an essential element for a superconducting magnet, that is to operate at a cryogenic temperature and sustain large magnetic forces. However, the contact pressures on the conductor, the spacers and the coil case, which are imposed in fabrication process, may be greatly reduced by relaxation at room temperature and by thermal contraction in the GFRP spacers during cool-down process. We therefore studied 61 kinds of commercial and test GFRPs and established a basis for suitable GFRP spacer material to be used in superconducting magnet windings. Glass transition temperature, T g , of the impregnating resin plays an important role in transverse creep deformation of GFRPs. GFRP spacers with T g above 423 K can maintain 80% of the initial pressure in a winding for two years at room temperature. This result was obtained by utilizing the transverse creep moduli of GFRPs at different temperatures and the time–temperature superposition principle. Transverse thermal contraction from 293 to 4 K decreases uniformly in all GFRPs as the resin weight content, R c , decreases. Also, contraction is smaller than that of the 304 stainless steel used for the coil case when R c is less than 15%. As a result, pressure decrease in the winding can be prevented during cool-down. The elastic modulus in the transverse direction of a GFRP is calculated by dividing the elastic modulus of the impregnating resin by R c . Fractures of the GFRPs at low temperatures are primarily in shear mode under four-point bending, in-plane compression, transverse compression, or interlaminar shear loading. Moreover, the transverse-compressive fatigue limit of plain-woven GFRP at low temperature depends on the maximum compressive stress of the cyclic loading under high mean-compressive stress and the stress range under low mean-compressive stress.

Shear/compressive strength of GFRP under mixed load condition at low temperature

Insulation of superconducting magnet systems requires excellent electrical insulating properties, compressive strength and flexibility so that it can bear the compressive stress of the electromagnetic force and the shear stress caused by the deformation of each conductor in these magnets. GFRP is suitable for these insulation systems and most superconducting magnet systems use it. Although the interlaminar shear strength of GFRP is about a tenth of its compressive strength, this strength increases under a combination of stresses. GFRP strengths under shear/compressive loading are specified for optimum designs. Therefore, we can apply GFRP against shear/compressive loading for which static and fatigue strengths are the dominant factors in magnet life assessment. The coefficient of friction of the surface affects the static and fatigue behavior at low temperature. Two types of tests were carried out to simulate the combined stresses, and shear/compressive static and fatigue tests were performed at 77 K on GFRP. Employing different angle test fixtures, GFRP specimens were loaded with various levels of shear and compressive stress. We evaluated the strength of insulators that sustain compressive and frictional shear stresses to take into account the stress redistributions for cases both with and without the occurrence of surface slips. A new criterion for the shear/compressive static and fatigue failure is proposed in this study.

Effect of Stress Ratio on Fatigue Crack Growth Threshold for Austenitic Stainless Steels in Air Environment

The fatigue crack growth threshold ΔKth is an important characteristic of crack growth assessment for the integrity of structural components. However, the accurate threshold ΔKth values for austenitic stainless steels in air environment are lacking in many fitness-for-service (FFS) codes, although fatigue crack growth tests have been performed and many test data had been published. This paper focuses on fatigue crack growth threshold ΔKth values for austentic stainless steel in air environment. The paper introduces the current ΔKth values provided by four major FFS codes and summarizes the available test data based on the literature survey. The paper then discusses the applicability of the existing ΔKth for stainless steels and proposes a new relation as a function of the stress ratio (the R ratio) for use by FFS codes.

Main Surface Crack Propagation and Crack Initiation and Propagation on Counter Plain Surface Under Cyclic Bending

Cyclic bending is a dominant loading mode in structures sustaining thermal loads. Under cyclic bending loads, a crack also initiates and propagates on the counter surface while the main crack grows. And then, these cracks meet and penetrate the thickness of the component. Numerical analysis was performed for the evaluation of the main elliptical crack propagation and crack initiation and propagation at the counter surface under cyclic out-of-plane bending. An inelastic three-dimensional finite element analysis took crack opening and closure into account. When the front surface is in tension, the main crack opens and the compressive strain on the counter surface increases. Thus, deeper the main crack, larger the total strain range on the counter surface and this stimulates crack initiation on the counter surface. As the main crack propagates, the J-integral range at the deepest point decreases for deeper than 40 % of the plate thickness, and the crack grows slower. On the other hand, the J-integral range of the counter surface crack increase rapidly and crack propagation rate of the counter crack becomes larger than that of the main crack. Both the cracks on front and counter surfaces meet near 2/3 of the plate thickness of the component. The calculated crack propagation rates in both longitudinal and depth directions of the main and the counter surface cracks based on the J-integral ranges are close to the experimental ones.Copyright

Fracture and Elevated-temperature Static-fatigue of Ceramics Containing Small Flaws

Studies concerning effects of flaw size on brittle fracture and elevated-temperature static-fatigue strengths are reviewed. Although ceramic materials fracture elastically, fracture stress has a nonlinear relation to flaw size, and the critical stress intensity factor for a small crack is lower than that for a large crack. The relationship is explained well by a fracture model, which takes into account the interaction between a flaw and the microstructure of the ceramic. A crack can be arrested below a certain stress level, i.e. below the static-fatigue limit. The static-fatigue limit also shows a nonlinear relationship to flaw size similar to that for brittle fracture. The effects of temperature, environment and material on static-fatigue limit are also discussed.