Fluid pressure response in poroelastic materials subjected to cyclic loading

When cyclic loading is applied to poroelastic materials, a transient stage of interstitial fluid pressure occurs, preceding a steady state. In each stage, the fluid pressure exhibits a characteristic mechanical behavior. In this study, an analytical solution for fluid pressure in two-dimensional poroelastic materials, which is assumed to be isotropic, under cyclic axial and bending loading is presented, based on poroelasticity. The obtained analytical solution contains transient and steady-state responses. Both of these depend on three dimensionless parameters: the dimensionless stress coefficient; the dimensionless frequency; and, the axial-bending loading ratio. We focus particularly on the transient behavior of interstitial fluid pressure with changes in the dimensionless frequency and the axial-bending loading ratio. The transient properties, such as half-value period and contribution factor, depend largely on the dimensionless frequency and have peak values when its value is about 10. This suggests that, under these conditions, the transient response can significantly affect the mechanical behavior of poroelastic materials.     

Surface hardness increase of 2024 aluminum alloy subjected to cyclic loading

Constant amplitude fatigue tests at R = 0.1, conducted on the aircraft aluminum alloy 2024 T3, have revealed an appreciable surface hardness increase of the alloy at the nano- and meso-scale during fatigue. The observed surface hardness changes could be monitored with confidence by means of nanoindentations. The degree of hardening increases with increasing number of fatigue cycles following exponential relations. With increasing fatigue stress level degree of hardening increases as well. The observed results provide a basis for developing concepts to early detect and also monitor fatigue damage accumulation in aluminum aircraft structures based on measurements of the material’s hardness changes by means of nanoindentations.     

Failure initiation in unnotched specimens subjected to monotonic and cyclic loading

Failure initiation in unnotched cylindrical bar specimens is predicted by application of the strain energy density theory. Maximum value of the local minimum strain energy density function is calculated, the critical value of which is assumed to coincide with failure by monotonic as well as cyclic uniaxial loading. Damage is accumulated in the specimen for each increment of monotonically rising load and each cycle of repeatedly applied load. Use is made of the incremental theory of plasticity to account for permanent deformation that is nonuniformly distributed throughout the cylindrical bar. Failure initiation site is found to occur at the center of the bar for monotonic loading where dilatation is dominant and near the specimen surface for fatigue loading where distortion is more significant. The results are consistent with the experimental observations without including microstructural effects. Nonhomogeneity caused by macro-dilatation and macro-distortion is also shown to play an important role in failure initation.     

Buckling of composite panels subjected to biaxial loading

Buckling loads and modes of flat composite laminates were measured and compared with theory. Laminates were subjected to simply supported boundary conditions and biaxial loading. Displacements were measured both mechanically using dial gages and optically using shadow moiré. Predictions were obtained numerically using the Galerkin method. Buckling loads were measured during 49 tests. Overall, measurements confirmed expected trends. Buckling loads increased with an increase in transverse tensile loading as predicted. Measured buckling modes were also well predicted, including an observed increase in mode number with an increase in transverse tensile loading. Measured buckling loads were not as well predicted, and substantial error was encountered during individual tests. Discrepancies between measurement and prediction are reported in terms of the percentage error in prediction. The average and standard deviation in percentage error for 49 measurements was 1.6 percent ±15.4 percent. These discrepancies are thought to be due to specimen imperfections, difficulties in simulating truly simply supported boundary conditions and/or nonuniform loading of the composite panels.     

A three-dimensional rectangular crack subjected to shear loading

In this paper a solution is derived to treat the three-dimensional elastostatic problem of a narrow rectangular crack embedded in an infinite elastic medium and subjected to equal and opposite shear stress distribution across its faces. Employing two-dimensional integral transforms and assuming a plane-strain solution across the width of the crack, the stress field ahead of the crack length is reduced to the solution of an integral equation of Fredholm type. A numerical solution of the integral equation and the corresponding mode II stress-intensity factor is obtained for several crack dimensions and Poisson's ratios of the material.     

Fatigue crack propagation life analysis of solder joints under thermal cyclic loading

Fatigue crack propagation life analysis of solder joints under thermal cyclic loadings was investigated by the strain energy release rate method using finite element analysis. A relationship between the crack-growth rate and the strain energy release rate was derived. Finite element simulations were carried out to investigate the effect of crack growth along the interface of solder and lead in a solder joint assembly. The crack propagation life of the solder joint with an interface crack was predicted from the derived relationship between crack growth rate and values of the strain energy release rate. It was found that crack propagation life is much higher than the crack initiation life.     

Efficient design sensitivities of structures subjected to dynamic loading

Calculation of design sensitivities often involves much computational effort, particularly in large structural systems with many design variables. Approximation concepts, which are often used to reduce the computational cost involved in repeated analysis, are usually not sufficiently accurate for sensitivity analysis. In this study, approximate reanalysis is used to improve the efficiency of dynamic sensitivity analysis. Using modal analysis, the response derivatives with respect to design variables are presented as a combination of sensitivities of the eigenvectors and the generalized displacements. A procedure intended to reduce the number of differential equations that must be solved during the solution process is proposed. Efficient evaluation of the derivatives, using finite difference and the recently developed combined approximations approach, is presented. Numerical examples show that high accuracy of design sensitivities can be achieved efficiently.     

The fatigue of aluminum alloys subjected to random loading

This paper describes an expeirmental investigation which was carried out to determine the fatigue life of two aluminum alloys (2024-T3 and 6061-T6). They were subjected to both constant-strain-amplitude sinusoidal and narrow-band random-strain-amplitude fatigue loadings. The fatigue-life values obtained from the narrow-band random testing were compared with theoretical predictions based on Miner's linear accumulation of damage hypothesis. Cantilever-beam-test specimens fabricated from the aluminum alloys were subjected to either a constant-strain-amplitude sinusoidal or a narrow-band random base excitation by means of an electromagnetic vibrations exciter. It was found that the ε-N curves for both alloys could be approximated by three straight-line segments in the low-, intermediate- and high-cycle fatigue-life ranges. Miner's hypothesis was used to predict the narrow-band random fatigue lives of materials with this type of ε-N behavior. These fatigue-life predictions were found to consistently overestimate the acutal fatigue lives by a factor of 2 or 3. However, the shape of the predicted fatigue-life curves and the high-cycle fatigue behavior of both materials were found to be in good agreement with the experimental results.     

Model analysis of box culverts subjected to highway loading

The strain distribution and the deflections of reinforced-concrete box culverts associated with highway loading are determined by testing scale models. Two types of scale models were constructured: 1/6-size concrete models and a 1/24-size photoelastic model. The concrete models were instrumented with electric-resistance strain gages, and the deflections were measured with dial indicators. Strain and deflection data due to live loading are compared with values from testing of prototypes. The results of testing indicate that box-culvert sections conforming to ASTM C 850 are overdesigned structurally. Testing of models of a redesigned box culvert indicates that they perform satisfactorily. Paper was presented in the Proceedings of the 1988 SEM Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading

Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading was studied by the testing of specimens made of C1045 steel and of annealed copper. Several theories were reviewed. A closed-form solution proposed by Mendelson¹² was used to predict external strains for open-end and closed-end thick-walled cylinders. An incremental theory proposed by Chu¹³ was used to provide incremental solutions for open-end thick-walled cylinders, and for cylinders subjected to nonproportionate loading. Test data for open-end and closed-end thick-walled cylinders made of C1045 steel and of annealed copper were in excellent agreement with the incremental theory. Larger values were predicted by use of the closed-form solution for circumferential strains than actual test data for open-end thick-walled cylinders at large depth of yielding. For cylinders subjected to nonproportionate loading, excellent agreement was indicated between the incremental theory and the experiments for the plot of axial load vs. circumferential strain for specimens made of both metals. Agreement between the incremental theory prediction of axial strains for the specimens made of annealed copper and test data is quite satisfactory. Larger values were predicted by the incremental theory for axial strain than experimental data for specimens made of C1045 steel. The error was conservative.     

Fracture mechanics of laminated glass subjected to blast loading

A failure criterion based on energy balance approach is introduced for the laminated glass panel subjected to blast loading. Based on this failure criterion, a damage factor is developed to assess the failure of the laminated glass panel. If the damage factor is less than one, the plate is safe otherwise unsafe. Trigonometric function is employed to express the transverse deflection and the Airy’s stress function in von Karman’s large deflection equations of a thin plate. The nonlinear ordinary differential equation of motion obtained using the Galerkin method is solved using Runge–Kutta method. The predicted results indicate that the breakages of the laminated glass may be caused by the negative phase of the blast load if the positive phase blast load is not violent enough to cause failure. Also, the size of glass shards the laminated glass plies breaks in to is predicted using the surface energy based failure model.     

Experimental investigation of circular cantilever beams subjected to impulsive loading

This paper reports the experimental results of quadrantal circular cantilever beam carrying a mass at its tip which is subjected to radial impact. It was observed that after impact a travelling plastic segment moved from the tip towards the root in a very short time, and when specimen reached the largest deformation, the beam whipped out evidently in the reverse direction. The curvature change of the curved beam reaches a peak value near the middle region of the beam and the maximum is at the root. The experimental results are compared with the solutions for the rigid-perfectly plastic model given in [12–13].The authors would like to thank Professor Yang Gui-tong for guidance and help.     

Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading

This paper analyses and models the dynamic interaction among permeable multi-cracks in a piezoelectric strip under anti-plane shear waves by the Schmidt method. The Fourier transform is applied and then two pairs of triple integral equations can be solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on not only the crack length and the piezoelectric coefficient, but also the thickness of the piezoelectric strip, the distance between multi-cracks and the frequency of incident wave.     

Extended displacement bound theorems for continua subjected to dynamic loading

Continua or structures made of elastic perfectly-plastic material subjected to variable loads which vary within the shakedown limits are considered, allowing for dynamic effects, such as inertia forces due to the loading conditions. A theorem bounding the residual deflection at any point is presented. Some interesting specializations to certain classes of dynamic loading are discussed.