Dilation and breakage dissipation of granular soils subjected to monotonic loading

Dilation and breakage energy dissipation of four different granular soils are investigated by using an energy balance equation. Due to particle breakage, the dilation curve does not necessarily pass through the origin of coordinates. Breakage energy dissipation is found to increase significantly at the initial loading stage and then gradually become sta-bilised. The incremental dissipation ratio between breakage energy and plastic work exhibits almost independence of the confining pressure. Accordingly, a plastic flow rule consid-ering the effect of particle breakage is suggested. The critical state friction angle is found to be a combination of the basic friction between particles and the friction contributed by par-ticle breakage.     

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.     

Elastic beam on a rigid frictional foundation under monotonic and cyclic loading

An elastic beam resting on a frictional foundation and loaded by the concentrated force or moment applied at its tip is considered. The evolution of slip zones along the beam is discussed for both monotonie and cyclic loading. It is shown that an infinite number of slip zones develop and their propagation satisfies in some cases a self-similarity property. Transient hysteretic effects under cyclic loading are discussed. The closed form analytical solution is presented for the elastic friction model in the case of monotonie loading.     

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 mechanism for longitudinally stiffened I girders subjected to patch loading

Investigation of the behaviour of plate girders (welded I girders) under the action of localized (patch) loading on a flange in the plane of the web is presented. Girders without vertical (transversal) stiffeners in the zone of load introduction, but with horizontal (longitudinal) stiffeners, are considered. An approximate solution for obtaining ultimate load is developed using failure (collapse) mechanism and following the upper bound theorem of plastic collapse. Procedure is based on the solution introduced by Roberts and Rocky and further elaborated by Roberts for the determination of the ultimate patch load for girders without longitudinal stiffeners. Procedure presented in this paper is adapted for the girders with longitudinal stiffeners. Proposed collapse mechanism is based on the experimental evidence. When the longitudinal stiffeners have enough rigidity, deformation at collapse, buckling of the web, is limited to the part of the web between loaded flange and longitudinal stiffener. Values of the ultimate loads obtained through developed procedure as well as the values from other, earlier authors’ proposal that was accepted and applied in the British standard BS 5400 are compared with the values from authors’ experiments and available database with the test results from other investigators.     

水下冲击波载荷作用下气背固支圆板动态毁伤实验

为了研究水下近爆载荷作用下舰艇水下结构的动态变形及失效毁伤模式,利用水下爆炸冲击波等效加载装置结合高速摄影技术,对两种厚度的气背固支5A06铝合金圆板进行了水下冲击波加载实验。得到了气背固支圆板塑性大变形、中心拉伸撕裂和边界剪切破坏3种典型失效模式的动态响应历程。比较分析了冲击波强度、冲击因子、损伤参数和响应参数4种毁伤判据对该类靶板毁伤模式的判别能力。实验结果表明:考虑了结构因素的损伤参数和响应参数能够更为全面的判别结构的失效毁伤情况。     

Estimates of the rupture life of structural components subjected to proportional cyclic loading

The process of creep in metals is associated with physical mechanisms which cause internal damage. This damage weakens the material; so that for a given stress level, the strain-rate increases with time. As a result of this behaviour, stress redistribution occurs which can greatly influence the ruptuie life of structural components. By use of the appropriate constitutive relations which model the tertiary portion of the creep curve, it is possible to estimate the life of a structural component by use of finite element methods. Unfortunately, the procedure is demanding on computer time; and, as a result, considerable attention has been given to the possibility of the use of bounding techniques which ease the computing problem and which are particularly useful at the early stage of design. Techniques have already been developed for bounding the rupture life of structural components subjected to constant loading and these are found to be useful. In this paper, bounding procedures are developed for structural components subjected to proportional cyclic loading. The results may be expressed in terms of a representative rupture stress, so that structural-component performance can readily be related to material behaviour.     

周期荷载作用下煤岩声发射特征的颗粒流模拟

为研究周期荷载应力水平对煤样声发射特征的影响,采用PFC数值软件开展了 3种不同应力水平的等幅周期荷载数值模拟试验,分析了周期荷载应力水平对煤样破坏循环次数、声发射计数及损伤演化特征的影响.研究结果表明:周期荷载作用下,煤样破坏过程中的声发射活动呈现初始、相对平静和活跃三阶段演化规律,且在煤样破坏前的周期荷载卸载阶段及...     

Fatigue and static strength of notched and unnotched aluminum-alloy and steel specimens

This paper describes a method of presentation of fatigue data on three commonly used aircraft materials, 2024-T3 and 7075-T6 aluminum alloys and normalized SAE 4130 steel, such that variations in fatigue strength with stress-concentration factor can be shown. Comparisons of the fatigue strengths of 2024-T3 and 7075-T6 aluminum are made for the most useful range of stress-concentration factors. Static-strength results of notched and unnotched specimens of the three materials are presented to show how the strength varies with some parameters of the stress concentration. Comparison of the data with one theory for the strength of cracked specimens was made.     

Failure modes of specimens containing surface flaws under cyclic torsion

Turbine-generator shafts are often subjected to a complex transient torsional loading. Such a torsional loading may initiate yielding at the outer radius of the shaft or in the fillets. The methods for predicting turbine-shaft fatigue life due to transient loading depent upon the mode of crack growth from an undetected crack. The most common location for the existence of a crack is the fillets or shoulders of the shaft. Specimens were designed from AISI 4340 steel with two diametrically opposed flat surfaces. Initial defect orientations of 0 deg, 45 deg and 90 deg with respect to the sepcimen axis on the fillet were studied. The specimens were subjected to cyclic torsion with zero mean torque and with a torque amplitude necessary to cause yielding at the outer radius of the specimen. When initial defects were aligned with a plane of maximum shear stress (0 deg and 90 deg), the cracks propagated along that plane. For 45-deg defects (aligned to a plane of maximum tensile stress) the crack still propagated along the plane of maximum shear. However, the number of cycles to initiate and to propagate the crack to failure for 45-deg defects were (two to three times) larger than those for 0-deg and 90-deg defects. Mode II and Mode III crack-growth rates were measured from specimens containing 0-deg and 90-deg defects. It was found that the crack-growth rate in Mode II was higher than in Mode III. However, all the specimens failed due to reduction of the net cross section, mostly attributed to Mode III crack growth. Similar results were obtained from specimens of turbine-shaft material (A469 steel), and 2024 aluminum with different rolling directions. Fatigue-crack-growth rates in Mode III were measured from circumferentially notched bar. They were found to be a unique function of ΔK _III alternating stress intensity in Mode III. It was found that the mechanism of crack growth is produced by the formation and linkage of elongated cavities at the crack tip.     

Fracture mechanics applications of absorbed specific fracture energy: Notch and unnotched specimens

The Absorbed Specific Fracture Energy (ASFE)^* is an energy criterion that may be applied to evaluate the embrittlement and fracture properties of low and medium strength structural materials. Some new results are presented to illustrate the application of ASFE, and relating them to the other fracture criteria such as J_1c and K_1c. A comparison of results is made for static and dynamic loading, and the influence of neutron irradiation.     

Notch strengthening in titanium aluminides under monotonic loading

An important concern for titanium aluminides is their limited ductility and its consequences for TiAl components containing stress concentrators. In recent experiments, evidence of notch strengthening has been found in one TiAl alloy under monotonic loading. The goal of this study is to fully explore this issue through tests on two cast alloys, one with a microstructure consisting of predominantly equiaxed gamma grains and the other having a fully lamellar microstructure. Tests involve monotonic tensile loading of notched specimens at room temperature under conditions of plane stress, where the notch radii are large relative to grain size. For each material, results from the testing of three notched specimen geometries are presented and finite element models are used to interpret the test results. This includes using the numerical models to apply Weibull statistical methods to predict notch strengthening in the specimens. It is shown that notch strengthening is clearly seen in both alloys tested and thus is likely to be a characteristic of TiAl alloys in general; however, strengthening is not as great as would be predicted by Weibull statistical methods as applied to brittle materials.     

Failure loads of spot weld specimens under impact opening and shear loading conditions

Failure loads of spot weld specimens are investigated under impact combined loading conditions. A set of test fixtures was designed and used to obtain failure loads of mild steel spot weld specimens under combined opening and shear loading conditions. Three different impact speeds were applied to examine the effects of separation speed on failure loads. Micrographs of the cross-sections of failed spot welds were obtained to understand the failure processes in mild steel specimens under different impact combined loads. The experimental results indicate that the failure mechanisms of spot welds are very similar for mild steel specimens at various impact speeds. These micrographs show that the sheet thickness can affect the failure mechanisms. For 1.0 mm specimens, the failure occurs near the base metal in a necking/shear failure mode. For 1.5 mm specimens, the failure occurs near the heat-affected zone in a shear failure mode. Based on the experimental results, the effects of the inertia force, the separation speed, and the loading angle on the failure loads of spot welds are investigated. Failure criteria are proposed to characterize the failure loads of spot welds under impact combined opening and shear loads for engineering applications. The failure load can be expressed as a function of the tensile strength of the base metal, the nugget size, the sheet thickness, the maximum separation speed, the loading angle, and empirical coefficients for a given welding schedule.     

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.     

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.     

Viscoplasticity theory based on overstress. The prediction of monotonic and cyclic proportional and nonproportional loading paths of an aluminum alloy

An isotropic formulation of the viscoplasticity theory for small strain and based on overstress with a differential growth law for the equilibrium stress is introduced. The four material constants and the two material functions of the theory are determined from uniaxial tensile tests involving strain-rate changes at room temperature and performed on a 6061 T6 Aluminum Alloy. Subsequently the theory is used to predict the biaxial behavior under axialtorsion loading. All tests are under strain control and involve proportional loading and axial followed by torsional straining (and vice versa). Cyclic histories include in-phase and out-of-phase cycling. The predictions of the theory are very reasonable for this cyclically neutral alloy. For cyclic hardening or softening materials a modification of the theory is necessary and is under development.     

A refinement of the shape of the temperature curve for cyclic loading of metal specimens

Some results are described of investigations to refine the shape of the temperature curve obtained when the thermal effect in cyclically loaded specimens is fixed. It is shown that the thermal effect occurs from the first loading cycles and not after application of a number of cycles, as previously assumed. A correlation is established between the temperature curve (its shape) and the shape of the curve for the change in the internal friction and the change in the bending of the specimen under cyclic loading. On this basis it can be stated that the shapes of the above curves indirectly describe the same changes in the metal when it is subjected to cyclic loads.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2 pp. 122–123, March–April, 1971.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.     

A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading

An extension of the upper bound shakedown theorem to load histories in excess of shakedown has been presented elsewhere in this issue. Here the minimisation process described therein is applied to the solutions of the ratchet limit as well as shakedown and limit load for a range of simple problems. The solutions provide an estimate of the maxima of the varying plastic strain magnitudes, which is compared with the Neuber approximate values. The position of the ratchet boundary is confirmed by comparison step-by-step analysis.     

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.