Lower-Bound Initiation Toughness with a Modified-Charpy Specimen

2009 ◽  
pp. 139-139-19
Author(s):  
RJ Bonenberger ◽  
JW Dally ◽  
GR Irwin
Keyword(s):  
Lower Bound ◽  
Charpy Specimen ◽  
Initiation Toughness

Lower-Bound Initiation Toughness of A533-B Reactor-Grade Steel

2009 ◽  
pp. 9-9-15
Author(s):  
GR Irwin ◽  
JW Dally ◽  
X-J Zhang ◽  
RJ Bonenberger
Keyword(s):  
Lower Bound ◽  
Initiation Toughness ◽  
Grade Steel

Technical Basis for Expansion of ASME BPVC Section XI, KIC Curve Applicability

2019 ◽  
Author(s):  
Hongqing Xu ◽  
Nathan Palm ◽  
Anees Udyawar
Keyword(s):  
Fracture Toughness ◽  
Lower Bound ◽  
Fracture Mechanics ◽  
Yield Strength ◽  
Room Temperature ◽  
Ferritic Steels ◽  
Initiation Toughness ◽  
Room Temperature Yield Strength ◽  
Class 1 ◽  
Technical Basis

Abstract When the Appendix G methodology, fracture toughness criteria for protection against failure, was first adopted by ASME Section III in 1972, it included a lower-bound Kir curve for ferritic steels with specified minimum room-temperature yield strength up to 50 ksi. In 1977, Section III Appendix G added a requirement to obtain fracture-toughness data for at least three heats (base metal, weld metal, and heat-affected zone) if the KIR curve is used for ferritic steels with specified minimum room-temperature yield strength between 50 and 90 ksi. The three-heat data requirement has not changed when the lower bound curve was adopted by Section XI, or when the lower-bound crack initiation toughness curve was changed from the dynamic Kir curve to the static KIc curve during the 2000s. Based on the accumulation of fracture-mechanics data of ferritic steels with specified minimum yield strength between 50 ksi and 90 ksi and their use for Class 1 pressure vessel production, Section XI recently expanded the applicability of the KIc curve to SA-508 Grade 2 Class 2, SA-508 Grade 3 Class 2, SA-533 Type A Class 2, and SA-533 Type B Class 2 whose specified minimum room-temperature yield strength is 65 ksi or 70 ksi. This paper describes the technical basis including the fracture-mechanics data to support the expansion of the applicability of the KIc curve by ASME Section XI.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

On the Crossing Number of $K_{m,n}$

10.37236/1748 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nagi H. Nahas
Keyword(s):  
Lower Bound ◽  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Crossing Number

The best lower bound known on the crossing number of the complete bipartite graph is : $$cr(K_{m,n}) \geq (1/5)(m)(m-1)\lfloor n/2 \rfloor \lfloor(n-1)/2\rfloor$$ In this paper we prove that: $$cr(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2$$ for sufficiently large $m$ and $n$.

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