NECKING OF A TENSION SPECIMEN

NECKING OF A TENSION SPECIMEN

VOLUME 25, NUMBER 4 APRIL, 1954 | M. S. PLESSET AND S. A. ZWICK
The chapter discusses the necking process of a tension specimen, where the velocity field is simple, allowing for a straightforward analysis of finite plastic deformation. The region $DOE$ moves as a rigid body with unit speed in the negative $y$ direction, while $D'OE'$ moves in the positive $y$ direction. The instantaneous plastic flow is restricted to the lines of discontinuity $D'D'$ and $EE'$. The stresses in the region $D''O''E''$ are determined by substituting $a^*$ for $a$ in the equations derived from (19). If the necking process continues without rupture, the central portion of the specimen will form two wedges with a slope of $1:2$ relative to the $x$ axis. The criterion for "sufficient depth" of the initial grooves is not precisely known, but for a parabolic groove, the length should be at least $4a$. The growth of a vapor bubble in a superheated liquid is influenced by liquid inertia, surface tension, and vapor pressure. As the bubble grows, evaporation occurs at the bubble boundary, reducing the temperature and vapor pressure within the bubble. The dynamic problem is linked with a heat diffusion problem, and a quantitative formulation is given for the radius of the vapor bubble as a function of time. The solution covers the range of physical interest, showing the strong effect of heat diffusion on bubble growth. Experimental observations in superheated water are compared with the predicted radius-time behavior, showing very good agreement. The analysis considers the bubble to be spherical, neglecting viscosity and compressibility effects. The temperature and pressure within the bubble are determined by the equilibrium vapor pressure and surface tension. The asymptotic solution for the bubble growth is derived, and the initial stages of bubble growth are described, including a delay period due to the cooling effect. The asymptotic behavior of the bubble growth is characterized by the limiting effect of heat diffusion on the bubble velocity. The theoretical predictions are compared with experimental data, showing good agreement.The chapter discusses the necking process of a tension specimen, where the velocity field is simple, allowing for a straightforward analysis of finite plastic deformation. The region $DOE$ moves as a rigid body with unit speed in the negative $y$ direction, while $D'OE'$ moves in the positive $y$ direction. The instantaneous plastic flow is restricted to the lines of discontinuity $D'D'$ and $EE'$. The stresses in the region $D''O''E''$ are determined by substituting $a^*$ for $a$ in the equations derived from (19). If the necking process continues without rupture, the central portion of the specimen will form two wedges with a slope of $1:2$ relative to the $x$ axis. The criterion for "sufficient depth" of the initial grooves is not precisely known, but for a parabolic groove, the length should be at least $4a$. The growth of a vapor bubble in a superheated liquid is influenced by liquid inertia, surface tension, and vapor pressure. As the bubble grows, evaporation occurs at the bubble boundary, reducing the temperature and vapor pressure within the bubble. The dynamic problem is linked with a heat diffusion problem, and a quantitative formulation is given for the radius of the vapor bubble as a function of time. The solution covers the range of physical interest, showing the strong effect of heat diffusion on bubble growth. Experimental observations in superheated water are compared with the predicted radius-time behavior, showing very good agreement. The analysis considers the bubble to be spherical, neglecting viscosity and compressibility effects. The temperature and pressure within the bubble are determined by the equilibrium vapor pressure and surface tension. The asymptotic solution for the bubble growth is derived, and the initial stages of bubble growth are described, including a delay period due to the cooling effect. The asymptotic behavior of the bubble growth is characterized by the limiting effect of heat diffusion on the bubble velocity. The theoretical predictions are compared with experimental data, showing good agreement.
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[slides and audio] THE GROWTH OF VAPOR BUBBLES IN SUPERHEATED LIQUIDS. REPORT NO. 26-6