In an earlier paper (1) an analysis was carried out to determine the stresses and deflection in an infinite strip plate undergoing large deflections when the plate was subjected to a combined normal loading and uniform temperature rise through the thickness, both of which were permitted to vary across the plate width. This paper extends the analysis and design charts to the case where the temperature distribution through the thickness of the plate may have any desired distribution. If the usual plate assumptions regarding plane sections remaining plane are valid, then the arbitrary temperature distribution can be represented completely by the average temperature and the first moment of the temperature about the plate middle surface, as far as the engineering stresses and deflections are concerned. The convenient nondimensional design charts cover equilibrium positions in the buckling as well as nonbuckling range and show maximum stress and central deflection as a function of pressure, average temperature, and temperature moment for cases of both clamped and simply supported edges.

In an earlier paper it was suggested that a knowledge of the elastic-stress variation in the neighborhood of an angular corner of an infinite plate would perhaps be of value in analyzing the stress distribution at the base of a V-notch. As a part of a more general study, the specific case of a zero-angle notch, or crack, was carried out to supplement results obtained by other investigators. This paper includes remarks upon the antisymmetric, as well as symmetric, stress distribution, and the circumferential distribution of distortion strain-energy density. For the case of a symmetrical loading about the crack, it is shown that the energy density is not a maximum along the direction of the crack but is one third higher at an angle ± cos −1 (1/3); i.e., approximately ±70 deg. It is shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a state of (two-dimensional) hydrostatic tension. As the distance from the point of the crack increases, the distortion strain energy increases, suggesting the possibility of yielding ahead of the crack as well as ±70 deg to the sides. The maximum principal tension stress occurs on ±60 deg rays. For the antisymmetrical stress distribution the distortion strain energy is a relative maximum along the crack and 60 per cent lower ± 85 deg to the sides.

Large deflection analysis is carried out to determine the deflections and membrane stresses for an infinite strip when subjected to pressure and temperature variations across the width of the strip with the end points fixed in space. Results are graphed for both clamped and simply supported edge conditions in the case of uniform temperature T 0 , and uniform pressure p 0 . The calculations also include the possible thermal buckling deflections. In the limit case of a membrane of width b and thickness h , subjected to this loading condition, the central deflection w 0 is determined from the simple relation [ ( w 0 / h ) 2 - 3 8 ( 1 + ν ) ( b / h ) 2 α T 0 ] ( w 0 / h ) = p 0 b 4 / ( 256 D h )

As an analog to the bending case published in an earlier paper, the stress singularities in plates subjected to extension in their plane are discussed. Three sets of boundary conditions on the radial edges are investigated: free-free, clamped-clamped, and clamped-free. Providing the vertex angle is less than 180 degrees, it is found that unbounded stresses occur at the vertex only in the case of the mixed boundary condition with the strength of the singularity being somewhat stronger than for the similar bending case. For vertex angles between 180 and 360 degrees, all the cases considered may have stress singularities. In amplification of some work of Southwell, it is shown that there are certain analogies between the characteristic equations governing the stresses in extension and bending, respectively, if ν , Poisson’s ratio, is replaced by − ν . Finally, the free-free extensional plate behaves locally at the origin exactly the same as a clamped-clamped plate in bending, independent of Poisson’s ratio. In conclusion, it is noted that the free-free case analysis may be applied to stress concentrations in V-shaped notches.

An electron paramagnetic resonance (EPR) method for monitoring the rate of atomic bond rupture in rubber subjected to uniaxial tensile strain in an ozone environment is described. The free radicals so formed are found to be quite stable and present in large, easily detectable concentrations. The initial rate of bond rupture was found to be approximately proportional to ozone concentration at fixed strain. Below a prestrain of three percent, no effect of the ozone environment was detected; above this threshold, the rate of rupture increases with strain up to strains of approximately 20 percent. It appears that this EPR technique is very sensitive and can yield information not readily obtainable by more conventional techniques.

Classical Kirchhoff bending solutions for a normally loaded elastically supported flat plate containing a semi-infinite straight crack are obtained using an integral equation formulation. Because the effects of initial spherical plate curvature are related to those of an elastic foundation, the solution can be applied to the problem of a crack in an initially curved unsupported plate as well. The explicit nature of the stresses near the crack point is found to depend upon the inverse half power of the nondimensional distance from the point, r/(D/k) 1/4 , where D is the flexural rigidity of the plate and k the foundation modulus. The particular case of an infinite strip containing the crack along the negative x-axis and loaded by constant moments M* along y = ±y* is presented. The inverse half-power decay of stress is additionally damped by an exponential factor of the form exp(−λy*/ 2 ).

Using a formulation in integral equations, a solution for the combined extension-classical bending stress and displacement solution is presented for the case of an infinite orthotropic flat plate containing a finite crack. While the solution can be expressed in closed form for the entire field, primary emphasis is placed upon the stresses near the crack point. Qualitatively, no major difference in behavior due to orthotropy was found although certain quantitative features are noted, mainly as a function of the characteristic rigidity ratio (E x /E y ) 1/2 . The inverse square-root character of the isotropic stress bending and extension is not changed by orthotropy, although amplitudes and distribution are affected. Account is taken of recent important work by Knowles and Wang dealing with Reissner bending of the plate which shows that the extensional and surface bending stresses are identical in singular character and circumferential distribution. A bending-extension interaction curve for fracture initiation is derived and shown to be linear when based upon the more exact bending theory.

Extending an earlier paper dealing with extensional stress distributions, this study considers the stresses around a crack point owing to bending loads. It is found first that the stresses possess the characteristic inverse square-root singularity in terms of distance from the crack point. Along the crack prolongation direction the symmetric principal stresses are of opposite sign and in the ratio (1 − ν)/(3 + ν), in contrast to the extensional situation where they are identically equal. This leads to the observation that more yielding might be expected as the percentage of bending to extension stress at the crack increases. In the antisymmetrical loading, the shear stress is a maximum ±90 deg to the side of the crack, where the distortion energy is also a maximum. Interesting reciprocity relationships are also shown to exist between the symmetrical and antisymmetrical loading conditions for the isochromatic fringe lines and the stress trajectories. Finally, the results are discussed in connection with the combined extensional and bending loading.