2286. On the Condition That the General Equation of the Second Degree Should Represent a Pair of Straight Lines

1952 ◽  
Vol 36 (316) ◽  
pp. 128
Author(s):  
B. D. Price
Keyword(s):  
General Equation ◽  
Straight Lines ◽  
Second Degree

Cryogenic Temperature Dependence of the Yield Strength of High-Strength Alloys

1966 ◽  
Vol 88 (1) ◽  
pp. 117-128 ◽  
Author(s):  
C. T. Yang
Keyword(s):  
Yield Strength ◽  
Stainless Steels ◽  
General Equation ◽  
Cryogenic Temperature ◽  
Elevated Temperatures ◽  
High Strength ◽  
Cryogenic Temperatures ◽  
Test Range ◽  
Titanium Nickel ◽  
Straight Lines

The effect of cryogenic temperatures (from 78 F to −423 F) on the yield strength of twenty alloys was studied. Experimental results prove that they do not conform to any of the following theories: Hollomon and Zener’s, Cottrell and Bilby’s, or Fisher’s. However, all the plottings in loge-loge scale of yield strength versus absolute cryogenic temperatures of these alloys fall on straight lines which are governed by one single general equation, σy = bT−m. From the Cottrell’s dislocation theory on yielding and Fisher’s equation of activation energy in forming a dislocation loop, the same type of equation of yield strength versus temperature as expressed by the empirical ones can be derived theoretically. The empirical equations are very useful in predicting yield strengths at any cryogenic temperature within or slightly out of the test range for which data were available. Some limited yield strength data at elevated temperatures for a few alloys were studied for comparison. It was observed the general equation for yield strength versus cryogenic temperatures holds valid for stainless steels but not so well for titanium, nickel, and aluminum alloys at elevated temperatures. However, no conclusion can be drawn until further detailed studies at elevated temperatures are made.

On the general equation of the second degree

Resonance ◽  
2015 ◽  
Vol 20 (7) ◽  
pp. 643-662 ◽  
Author(s):  
S. Kesavan
Keyword(s):  
General Equation ◽  
Second Degree

Note on the General Equation of the Second Degree

1900 ◽  
Vol 7 (10) ◽  
pp. 217
Author(s):  
George R. Dean
Keyword(s):  
General Equation ◽  
Second Degree

scholarly journals II. On a special form of the general equation of a cubic surface and on a diagram representing the twenty-seven lines on the surface

1894 ◽  
Vol 185 ◽  
pp. 37-69
Keyword(s):  
Special Form ◽  
General Equation ◽  
Mathematical Journal ◽  
Third Order ◽  
Cubic Surface ◽  
The Third ◽  
Straight Lines

The existence of straight lines on a cubic surface, the number of them, and their relations to each other was first discussed in a correspondence between Salmon and Cayley. In a paper which appeared in 1849, in vol. 4 of the ‘Cambridge and Dublin Mathematical Journal,’ “On the Triple Tangent Planes of Surfaces of the Third Order,” Cayley gave a sketch of what was then known, and gave the equations of the forty-five planes in which the twenty-seven lines on the surface lie by threes, when the equation of the surface is taken in a particular form.

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