• Honam Mathematical Journal
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• v.27 no.4
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• pp.595-602
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• 2005

Comtrans algebras are modules equipped with two trilinear operations: a left alternative commutator and a translator satisfying the Jacobi identity, the commutator and translator being connected by the so-called comtrans identity. These identities have analogues for trilinear forms. On a given vector space, the set of all comtrans algebra structures itself forms a vector space. In this paper, the dimension of the space of comtrans algebra structures on a finite-dimensional vector space is determined.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.2
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• pp.208-214
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• 1986

To establish the evaluation of the fatigue crack growth behavior in 5083-O aluminum alloy, constant load-amplitude fatigue crack growth tests were carried out under the small scale yielding conditions. Crack length and closure of this material were measured by the compliance method using a clip-on gage. The main results obtained as follows: The fatigue crack growth rate against stress intensity factor range .DELTA.K exhibits the trilinear form with two transitions at the growth rate 5.5*10$^{-6}$ and 5.5*10$^{-5}$ mm/cycle, in the so-caled Region II. The trilinear form appears still in the plot of growth rate versus effective stress intensity factor range .DELTA. $K_{eff}$. Stress ratio R affects the relationship of crack growth rates versus .DELTA.K but does not affect the reation of crack growth rate versus .DELTA. $K_{eff}$. The experimental results indicate that the effective stress intensity range ratio U depends on the maximum stress intensity factor $K_{max}$, but not on the stress ratio R.o R.R.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.2
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• pp.271-277
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• 1988

The threshold fatigue crack growth and the stable crack propagation behaviors were studied in 7017 T 651, 7020 T 651 and 5083 H 115 aluminum alloys. The threshold (.DELTA. K $_{th}$) fatigue crack growth can be expressed by the equation .DELTA. $K_{th}$) = .DELTA. $K_{tho}$(1-R)$^{r}$ , where R is stress ratio, .DELTA. $K_{tho}$ is .DELTA. K at R = 0 and r is material constant. The stable crack growth rate against stress intensity factor range .DELTA. K exhibits the trilinear form with two transitions and results of investigation on crack closure phenomena showed that the crack opening stress intensity factor $K_{op}$ is approximately equal to R $K_{max}$. + .DELTA. K $_{th}$.th/.