THERMAL ELASTIC-PLASTIC STRESS ANALYSIS OF STEEL WOVEN REINFORCED ALUMINUM METAL–MATRIX COMPOSITE LAMINATED PLATES

In this study, an elastic-plastic stress analysis is carried out on symmetric cross-ply [0°/90°]₂ and angle-ply [30°/?30°]₂, [45°/?45°]₂, [60°/?60°]₂ steel woven reinforced aluminum metal–matrix laminated plates under thermal loads varying linearly along the thickness. Laminated composite plates are simply supported and subjected to linear temperature change through the thickness as T ₀ at the upper and lower surfaces and T at the middle plane, respectively. An analytical solution is performed for satisfying thermal elastic-plastic stress–strain relations and boundary conditions for small plastic deformations. The composite materials are assumed to be linearly hardening. The Tsai–Hill criterion is used as a yield criterion. Plastic and residual stress distributions along the thickness of the plates are obtained. Plastic and residual stress components, σ _x ) _p , (σ _y ) _p and (σ _x ) _r , (σ_y) _r , have some magnitude but (τ _xy ) _p and (τ _xy ) _r are zero for all stacking sequences. All the residual stress components are in static balance with respect to the middle plane of the laminates since they are symmetric in opposite signs. The magnitude of the residual stress components is the highest at the upper and lower surfaces.     

ELASTIC‐PLASTIC DEFORMATION OF A CENTRALLY HEATED DISK

The subject of this investigation is stress, displacement, and plastic strain in a centrally heated elastic‐plastic disk. The material is assumed to obey Tresca's yield criterion and its associated flow rule and to exhibit linear strain hardening. Due to the loading under consideration, plastic flow sets in at the center of the disk in a “corner-regime” of Tresca's hexagon, and, as in related cases, the plastic core is composed of two parts, the outer lying in a “side-regime.” For a special hardening parameter, explicit expressions for stress, displacement, and plastic strain are derived. With increasing core temperature, a second plastic zone forms at the edge of the disk.     

FREE VIBRATION OF HEATED EULER–BERNOULLI BEAMS WITH THERMAL POSTBUCKLING DEFORMATIONS

Based on the accurate geometrical nonlinear theory for Euler–Bernoulli beams, considering the coupling of the longitudinal and transverse motions, the harmonic responses of small vibration of uniformly heated beams with and without static thermal postbuckling deformations are presented by employing the numerical shooting technique. Characteristic curves of the lower order frequencies versus the temperature parameter are illustrated for pinned-pinned, fixed-fixed, and also pinned-fixed boundary constraints. The numerical results show that all the frequencies of unbuckled beams decrease continuously with the increment of the temperatures rise. However, when the beam is in a postbuckled state, all the lower frequencies increase along with the increment of temperature, except for the third- and the fourth-order frequencies of the pinned-pinned beam.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 3: TEMPERATURE DEPENDENCY OF ELASTIC MODULI FOR SEVERAL METALS AT TEMPERATURES FROM -196 TO 1000° C

The temperature dependency of the dynamic moduli of elasticity of steel and aluminum and copper alloys was investigated experimentally by an ultrasonic-wave method, in the temperature range from —196 to 1000°C. The results are compared with those obtained by the resonant-frequency method and are represented as empirical formulas. Useful data for commercial alloys are given in tables, by chemical composition.