# Spin tests to determine brittle fracture under plane strain

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## Abstract

The feasibility of using cyclic thermal stress or hydrostatic pressure to generate a fatigue crack in a large test-rotor blank is demonstrated. Test rotors, having test notches with fatigue-crack terminations, were spun to fracture to determine optimum test-notch design. It was found that, for the other test-notch dimensions held, it was necessary to extend the fatigue crack a minimum of 0.1 in. from the machined portion of the test notch to obtain a most effectively notched test rotor. In another series of tests, the influence of temperature on brittle-fracture strength of a Cr-Mo-V steel under plane strain was evaluated. It was found that, although there is a significant increase in fracture strength with increasing temperature, no knee in the curve is apparent in the vicinity of the conventionally measured transition temperatures of*NDT* and*T*_{50}. Also, design against brittle fracture is still required at temperatures above*NDT* and*T*_{50}.

## Keywords

Fatigue Mechanical Engineer Brittle Transition Temperature Fluid Dynamics## Nomenclature

*C*notch length of test rotor (total), in

*E*modulus of elasticity, psi

*e*elongation in 2-in. gage length, percent

*G*_{C}fracture toughness of material,\(\begin{gathered} \hfill \\(\pi \sigma _o ^2 C/2E) (1 - \nu ^2 ) \hfill \\ \end{gathered} \), in. lb/in.

^{2}*G*_{IC}fracture toughness of material under plane strain,\(G_c /[1 + (1.4/\alpha _1 ^2 )]\), in. lb/in.

^{2}*h*length of test rotor, in

*K*_{IC}stress-intensity factor under plane strain,\(10^{ - 3} [EG_{IC} /(1 - \nu ^2 )]^{1/2} ,ksi\sqrt {in.} \)

*l*length of fatigue crack forming one of the test-notch terminations, in

*N*fracture speed of test rotor, rpm; ω=2π

*N*/60, rad/sec*NDT*nil-ductility transition temperature, °F

*R*_{i}inside radius of test rotor, in.; ID=2

*R*_{ i }, in*R*_{i}outside radius of test rotor, in.; OD=2

*R*_{ o }, in*RA*reduction of area, percent

*T*test temperature, °F

- Δ
*T* temperature difference between that at the hole wall and that remote from the hole, °F

*T*_{50}Charpy Vee-notch 50-percent shear-fracture appearance transition temperature, °F

- α
thermal coefficient of expansion, (in./in.)/°F

- α
_{1} constraint index,\(h\sigma _{y^2 } /EG_C \), dimensionless

- ε
strain at the hole wall, 10

^{2}σ/*E*, percent- ν
Poisson's ratio=0.3 (for steel)

- ρ
mass density of material, lb sec

^{2}/in.^{4}=0.283/386- σ
tangential stress at the hole wall,

*E*αΔ*T*/(1−ν), psi- σ
_{aν} average net-section tangential stress corresponding to the fracture speed of the test rotor,\(\frac{{\rho \omega ^2 }}{3}(\frac{{R_o ^3- R_i ^3 }}{{R_o- C/2}}),psi\)

- σ
_{o} nominal fracture stress. Tangential stress at center of solid rotor corresponding to the fracture speed of the test rotor,\(\frac{{(3 - 2\nu )}}{{8(1 - \nu )}}\rho \omega ^2 R_o ^2 \), psi

- σ
_{4} nominal stress correction for uniform

*C*of 4.0 in.,\(\sigma _o (C/4)^{1/2} \)- σ
_{IO} nominal fracture stress for conditions of complete plane strain and

*C*=4 in.,\(\alpha _4 /(1 + \frac{{1.4}}{{\alpha _1 ^2 }})^{1/2} \), psi- σ
_{y} yield strength of material, psi (0.2-percent offset)

- σ
_{u} ultimate strength of material, psi

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## References

- 1.
*Irwin, G. R., “Fracture Mode Transition for a Crack Traversing a Plate,” Met. Eng. Conf., ASME, Albany, N. Y. (April 29–May 1, 1959)*.Google Scholar - 2.
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*Winne, D. H. and Wundt, B. M., “Application of the Griffith-Irwin Theory of Crack Propagation to the Bursting Behavior of Disks, Including Analytical and Experimental Studies,” Trans. ASME*,**80**, (*1958*).Google Scholar - 6.
*Clark, W. G., Jr., and Ceschini, L. J., “Fatigue Precracking of Spin-Burst Toughness Specimens,” presented at SESA Spring Meeting, Paper No. 1357A, Albany, N. Y. (May 7–10)*.Google Scholar