Failure of spot welds under in-plane static loading

Under in-plane loading conditions, two independent modes contribute to the failure of a spot weld: the in-plane shear mode and the in-plane rotational mode. In this work, the failures of both modes under large static load are examined individually. To study the combined failure of these two modes, two special test coupons are designed. The first coupon contains one spot weld. The second coupon contains five spot welds. Tests conducted in this work show that a very simple force-based failure criterion can be used to predict the failure of a spot weld under large in-plane combined static loads. Current multiaxial failure theory cannot explain this combined failure. This force-based spot weld failure criterion fits current automotive industry needs for body shell finite element application very well.     

Elastic stability of flat spiral springs

Summary This paper deals with the elastic stability of the flat spiral spring, that is, a structure consisting of a wire coiled into a spiral lying in a plane. A rough calculàtion valid for spiral springs having a large number of coils shows that the critical number of turns which the spring has to be wound or unwound to reach the state of instability is determined only by the ratio of the sides of the rectangular wire section. It depends neither upon the number of coils nor upon Young's modulus of the wire material.In order to verify in how far this holds for a spring with a small number of coils a second and more accurate calculation is given, though for a (fictitious) spiral spring having circular and identical coils only. Further, it is shown that the realization of a spiral spring able to undergo more than, say, three turns without becoming unstable is impossible. A survey of the results is given at the end of the paper.     

Grip pressure distribution under static and dynamic loading

The dynamic response of a vibrating handarm system is strongly related to the grip force. While the relationship between total grip force and vibration characteristics of the hand-arm system has been extensively studied, no attempts have been made to investigate the distribution of grip pressure at the hand-handle interface. The local grip-pressure distribution may be more closely related to the finger blood flow, fatigue and loss of productivity than total grip force. In the present study, distribution of static and dynamic forces at a hand-handle interface is investigated using a grid of pressure sensors mounted on the handle. The pressure distribution is acquired for different values of static and dynamic grip forces in the range of 25–150 N. The dynamic measurements were conducted at various discrete frequencies in the 20–1000 Hz range with peak acceleration levels of 0.5 g, 1.0 g, 2.0 g and 3.0 g. The grip-pressure distribution under static loads revealed a concentration of high pressures near the tips of the index and middle fingers, and the base of the thumb. This concentration of high pressures shifted towards the middle of the fingers under dynamic loads, irrespective of grip force, excitation frequency and acceleration levels. These local pressure peaks may be related to impairment of blood flow to finger tips and the possible causation of vibration white finger. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Study of the mechanical properties of plain concrete under dynamic loading

A new testing methodology based on the Hopkinson bar principle is proposed for studying globally and locally the mechanical properties of plain concrete at a high strain rate. A Hopkinson bar bundle measures the local mechanical characteristics over the cross section of a large specimen of plain concrete subjected to impact loading. With this method, more accurate measurements of the stress-strain diagram are obtained, especially during the fracturing phase of the concrete specimen.     

The kinetics of creep embrittlement under long-term static loading

The formulation and solution technique for the problem of construction of evolutionary equations of creep embrittlement of metal materials are considered. Embrittlement is regarded as loss of plasticity depending on the time to fracture. Experimental data for high-temperature steels and alloys are systematized and analyzed, and, on this basis, two main classes of materials, those that are subjected to ductile fracture and those that undergo embrittlement, are singled out. The kinetics of embrittlement is considered as regards the strain of instantaneous fracture and obeys the power law. The conditions of change in the nature of fracture are formulated, which allows one to calculate the coordinates of the inflection points on delayed-fracture curves. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 104–113, June, 2000.     

Variational analysis of gradient elastic flexural plates under static loading

Gradient elastic flexural Kirchhoff plates under static loading are considered. Their governing equation of equilibrium in terms of their lateral deflection is a sixth order partial differential equation instead of the fourth order one for the classical case. A variational formulation of the problem is established with the aid of the principle of virtual work and used to determine all possible boundary conditions, classical and non-classical ones. Two circular gradient elastic plates, clamped or simply supported at their boundaries, are analyzed analytically and the gradient effect on their static response is assessed in detail. A rectangular gradient elastic plate, simply supported at its boundaries, is also analyzed analytically and its rationally obtained boundary conditions are compared with the heuristically obtained ones in a previous publication of the authors. Finally, a plate with two opposite sides clamped experiencing cylindrical bending is also analyzed and its response compared against that for the cases of micropolar and couple-stress elasticity theories.     

Influence of specimen-reconstituting method on the undrained response of loose granular soil under static loading

This paper describes the results of an experimental study on the undrained shear behaviour of loose sand collected from the location close to the epicenter of the recent Chlef (Algeria) Earthquake (October 10,1980).The study focuses on the effects of the mode of the soil deposition on the liquefaction resistance of the Chlef sand.For this purpose,the results of undrained monotonic triaxial compression tests performed on samples with initial density of 0.29 under initial confining pressures ranged from 50 kPa to 200 kPa are presented.The specimens were prepared by two depositional methods namely dry funnel pluviation and wet deposition.It was found that there was a marked difference in the undrained behaviour of sand in terms of maximal deviatoric stress,peak strength,residual strength and excess pore water pressure,even though the density and stress conditions were identical.The conclusion was that the soil fabric was responsible for this result.The results indicated also that at low confining pressures,the specimens reconstituted by the wet deposition method exhibited complete static liquefaction (zero effective confining pressure and zero stress difference).     

Frictional Hertzian contact problems under cyclic loading using static reduction

In this study we investigate an axisymmetric Hertzian contact problem of a rigid sphere pressing into an elastic half-space under cyclic loading. A numerical solution is sought to obtain a steady state, which demands a large amount of computer memory and computing speed. To achieve a tractable problem, the current numerical model uses a “static reduction” technique, which employs only a contact stiffness matrix rather than the entire stiffness of the problem and is more accurate than the approach used by most finite element codes. Investigation of the tendency of contact behavior in the transient and steady states confirms that a steady state exists, showing converged energy dissipation. The dependence of dissipation on load amplitude shows a power law of load amplitude less than 3, which may explain some deviations in the experimental findings.     

The basal slip in zinc under static and dynamic loading

This paper presents the results of an investigation of static and dynamic shear behaviour of two purities of zinc single crystals. All the crystals tested were in the form of cylindrical rods with the [0001] crystallographic direction parallel to the rod axis. The static tests were performed by applying simple transverse shear loading in one of the slip directions to one end of the crystals with the other end of the crystals rigidly clamped. The static shear stress vs. shear strain relations are obtained from these tests. The dynamic tests were conducted by suddenly stopping (within a period of about 25 × 10⁻⁶ sec) one end of the crystals which were moving in the slip direction with various velocities. The resulting waves of plastic shear deformation which propagate from the stopped ends of the crystals toward the free ends are analysed. The analysis is based upon the assumption that elastic strains may be neglected in comparison with the plastic strains. The use of the results of this analysis in conjunction with measurements of the permanent lateral deflections of the crystals resulting from the dynamic tests leads to the determination of dynamic shear stress vs. shear strain relations.The results of this study show that the stress required to produce a given permanent basal shear strain in single crystals of zinc is considerably greater under the dynamic conditions employed than under static conditions. This stress decreases with increasing temperature.     

Damage accumulation stages in polycrystalline duralumin under static fatigue loading

Two groups of mode changes in the internal structure of a cyclically loaded tension specimen containing a circular hole are analyzed. Their association with order-dependent parameters are also identified. Solutions are obtained and they show that stage I and II deformation in the vicinity of a macroscale stress concentrator is caused by an occupation wave where the velocity is bounded below certain limiting value. Stage III deformation occurs in the strain-localization region.     

Experimental observations of tyre deformation characteristics on heavy mining vehicles under static and quasi-static loading

Due to large sidewall and bead thicknesses, multi-piece rims are necessary for use with large off-the-road (OTR) tyres. This paper presents the testing protocol and observed load/deflection and vertical/sidewall deflection characteristics of three Goodyear OTR tyre assemblies, namely, (1) a radial 29.5R29 (2) a bias-ply 29.5-29, and (3) a bias-ply 26.5-26. Localized tyre deformations and rim displacements were measured using optical displacement transducers and post-processing high-speed camera images using digital image analysis software. A validation analysis illustrated a maximum difference of 4.05% of vertical wheel displacements between the aforementioned methods. Quasi-static tests show the maximum values of vertical rim displacement and lateral tyre deflection are in the range of 72.2–78.9 mm and 23.3–27.1 mm, respectively, for a severe excitation condition. Differences ranging from 0.2% to 21.5% for maximum vertical and lateral tyre deflections were found between static load tests and engineering data provided by the tyre manufacturer. Linear relationships were observed for both vertical wheel displacement and lateral tyre deflection versus load for all tests. This study demonstrates a thorough methodology to study deflection characteristics of heavy duty OTR tyres and the collected data could be very useful in the development of numerical models of wheel and tyre assemblies for mining vehicles.     

Viscoelastic properties of MR elastomers under harmonic loading

This paper presents both experimental and modeling studies of viscoelastic properties of MR elastomers under harmonic loadings. Magnetorheological elastomer (MRE) samples were fabricated by mixing carbonyl iron power, silicone oil, and silicone rubber and cured under a magnetic field. Its steady-state and dynamic properties were measured by using a parallel-plate rheometer. Various sinusoidal loadings, with different strain amplitude and frequencies, were applied to study the stress responses. The stress–strain results demonstrated that MR elastomers behave as linear visocoelastic properties. Microstructures of MRE samples were observed with a scanning electron microscope. A four-parameter linear viscoelatic model was proposed to predict MRE performances. The four parameters under various working conditions (magnetic field, strain amplitude, and frequency) were identified with the MATLAB optimization algorithm. The comparisons between the experimental results and the model predictions demonstrate that the four-parameter viscoelastic model can predict MRE performances very well. In addition, dynamic properties of MRE performances were alternatively represented with equivalent stiffness and damping coefficients.     

表面裂纹准静态扩展的有限元模拟计算

由于现有断裂准则未能考虑表面裂纹前沿各点实际断裂阻力的变化，所作的表面裂纹准静态扩展模拟计算不能很好地预测几何形貌的真实变化规律。本文提出了一个考虑应力状态不同对实际断裂阻力影响的变阻力断裂准则；并以该准则作为表面裂纹前沿局部断裂扩展的判据，通过三维有限元法进行了表面裂纹准静态扩展的模拟计算；还将模拟预测值与用多试件法测得的实验值进行比较，验证了变阻力断裂准则作为裂纹稳态扩展判据的有效性     

Failure loads of spot welds under combined opening and shear static loading conditions

Failure loads of spot welds are investigated under combined opening and shear static loading conditions. Square-cup specimens were used to obtain the failure loads of mild steel spot welds under a range of combined opening and shear loads. Optical micrographs of the cross-sections of spot welds before and after failure were examined to understand the failure processes under different combinations of loads. The experimental results indicate that under nearly pure opening loads, shear failure occurs in the heat affected zone along the nugget circumferential boundary. Under combined opening and shear loading conditions, necking/shear failure starts near the nugget in the stretching side of the base metal sheet. According to the experimental observations, a simple lower bound limit load analysis is conducted. The results of the lower bound limit load analysis quantitatively agree with those of the experiments. A simple closed-form equation is proposed to characterize the failure loads of spot welds under combined opening and shear static loading conditions. The failure load is expressed as a function of the tensile strength of the base metal, the nugget size, the sheet thickness, the loading angle for characterization of combined loads, and an empirical coefficient for the given welding schedule.     

Stability and limit states of elastoplastic spherical shells under static and dynamic loading

The problem of elastoplastic deformation, buckling, and postcritical behavior of spherical shells is solved using a finite element method and a cross-type explicit scheme of time integration. Stability problems for hemispherical shells under external pressure and compression between rigid plates are considered. The influence of holes and boundary conditions on shell deformation is investigated. It is shown that the calculation results are in good agreement with experimental data.