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By J.H. Jeans, M.A., F.R.S

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8; b) J values increase about 10-14% by considering the pressure acting on crack surfaces, and c) KI values calculated by these analyses agree well with the results by A. S. Kobayashi. 2) A new definition of the J-integral in multi-phase materials is proposed and the path independent cahracteristics of this new J-integral is verified. , "The Continuum Theory of Lattice Defects", Prog. 94-98. , " A Simple Procedure for Estimating Stress Intensity Factor in Region of High Stress Gradient", Proc. S.

Note that the maximum value is reached in a short time after the application of thermal loading [12]. J-integra1 of the pre10aded specimen We consider the case that the eigen strains are composed of plastic strains, i. , e:1. • Equation (17) leads to JTi (au i l aX1 Jdr r +JJcr1-J.. /ax1 JdA (29) A or .. (ae:1-J. /aX1 JdA JJcr1-J A where e: 1 • '''J.. = e:~1-J• - JT. /ax1 Jdr 11- (30) r + e:~. , and inertia forces are neglected. 1-J The J-integra1 of a center cracked plate subjected to the remotely uniform stress, (J 0' as shown in :F'ig.

Second, a new definition of the J-integra1 in multi-phase material is proposed. The new J-integra1 has path independent charecteristics. Several examples are analyzed. 1. INTRODUCTION In the present work, the J-integra1 is extended and applied to cracking in a pressure vessel of a reactor. The J-integra1 is used widely in fracture mechanics, but several shortcomings must be overcome for its use in the safety design of reactors: (1) Since the crack in a reactor has three dimensional shape, the evaluation of a three-dimensional J-integra1 is required.

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An Elementary Treatise on Theoretical Mechanics by J.H. Jeans, M.A., F.R.S

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