Strain Effect of Manganin Transverse Piezoresistive Gauge and Measurement of Dynamic Transverse Stresses

Manganin piezoresistive gauges have been extensively used in dynamic stress measurement for decades.It is noted,however,that when used to measure transverse stresses,considerable strain effect is caused as the consequence of change of electrical resistance resulted from bending of wires in the longitudinal-strain-experiencing sensing element of the gauge,a phenomenon discussed in this paper theoretically as well as experimentally.This effect yields unwanted signals to blend with output piezoresistive signals and is not negligible,hence decreases measurement accuracy sizably if not properly handled.To overcome this drawback,a new type of manganin transverse piezoresistive gauge has been developed by authors of this paper,which can reduce the resistance increment to acceptable low level so as to effectively bring the adverse effect under control.

COPLANAR CRACKS IN A FINITE TRANSVERSELY ISOTROPIC ELASTIC SLAB UNDER ANTIPLANE SHEARL STRESSES

An antiplane crack problem concerning a pair of coplanar cracks in a finite transversely isotropic elastic slab is considered. Using Fourier integral transform together with singular integral equation which can be solvel numerically by suing a collocation technique. Once the integral equation is solved, the relevant crack energy and stress intensity factors of the problem are given. The analysis present can be easily extended to include cases where there are two or more pairs of coplanar cracks in the slab.

TWO COPLANAR CRACKS IN A TRANSVERSELY ISOTROPIC ELASTIC SLAB SUBJECTED TO ANTIPLANE SHEAR STRESSES

The problem of a transversely isotropic elastic slab containing two coplanar cracks subjected to an antiplane deformation is considered. With the aid of an integral transform technique, we formulate the problem in terms of a finite-part singular integral equation which can be solved numerically, Once the integral equation is solved, relevant quantities such as the crack energy can be readily computed.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

TRANSVERSELY ISOIROPIC BEAM UNDER INITIAL STRESS

Starling from Novozhilov's nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.

An analytical model for predicting sheet springback after V-bending

Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simu-lating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.

Numerical Si mulation of Inner Stress Fields for Stretching Block With Rectangular Section Between Flat Anvils

The stretch of blocks with rectangular section using flat anvils was simulated by using ANSYS software. The inner stress distribution for different tool width ratio w/h and blank width ratio b/h was studied. Consequent- ly, critical anvil width ratio （w/h）c and critical blank width ratio （b/h）c are obtained, which provide a sound basis for designing reasonable stretching technology.

Dynamic Shear Stress Measurements of PMMA

In this paper,experiments of one-dimensional plane plate impact on polymethylmethacrylate（PMMA） targets are conducted,in which dynamic transverse stresses induced in the targets are measured using a new type of manganin piezoresistive stress gauge having 50 Ω low-pressure narrow grid-like foil.It is shown that this new instrument can improve measurement accuracy remarkably by reducing the so-called strain effect.Moreover,relationship between shear stress and longitudinal stress within a certain range of the latter is obtained.

An advanced higher-order theory for laminated composite plates with general lamination angles

This paper proposes a higher-order shear deformation theory to predict the bending response of the laminated composite and sandwich plates with general lamination configurations.The proposed theory a priori satisfies the continuity conditions of transverse shear stresses at interfaces.Moreover,the number of unknown variables is independent of the number of layers.The first derivatives of transverse displacements have been taken out from the inplane displacement fields,so that the C 0 shape functions are only required during its finite element implementation.Due to C 0 continuity requirements,the proposed model can be conveniently extended for implementation in commercial finite element codes.To verify the proposed theory,the fournode C 0 quadrilateral element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate.Numerical results show that following the proposed theory,simple C 0 finite elements could accurately predict the interlaminar stresses of laminated composite and sandwich plates directly from a constitutive equation,which has caused difficulty for the other global higher order theories.

A Nonlinear Dynamical Theory of Non-Classical Plates

In ths paper. a new nonlinear formulation of plates. including shear and rotatory inertia and transverse normal stress effects, is developed by means of general assumptions, of which the von Karman-type formulation and some thick plate theories are special cases. To keep the formulation fairly general, the problem addressed in this paper simultaneously includes: the effects of shear deformation according to the geometric deformation similarity of the crosssection, the rotatory inertia, and the transverse normal stress. The three-dimensional compatible equations are applied to derive the basic equations. Numerical results are given for linear and non-linear analysis of plates.

Study on strip buckling in continuous annealing lines/hot galvanizing

In continuous annealing lines/hot galvanizing,strips are guided by upper and lower rolls in an alternate up and down vertical motion.This kind of process consisting of heating,soaking,and cooling furnaces(or zones) has several advantages in terms of productivity and product quality.Main problems encountered in continuous annealing lines are misguiding and formation of buckling.The strip buckling causes the strip to be rejected and,in the worst case,the strip breaks and the continuous annealing lines are compelled to stop.In this paper the elastic-plastic model of the strip traveling and the corresponding boundary condition were constructed dependant on the theory of mechanic.Simulations are performed in two steps.First,a homogeneous longitudinal tensile stress is applied at one end of the strip,the other end of the strip and the roll are restricted.In the second step,the applied tension remains constant.A uniform displacement is applied to the other end of the strip and a rotation to the roll. The transverse compressive stress,the buckling formation during strip traveling process,the location for the buckling taking place and the buckling criterion were investigated systematically.The result shows that the transverse compressive stress increases with the increase of the tensile stress and the crown of the tapered roll. Because the contact area between the tapered roll and the strip increase with the decrease of the crown,the tensile stress distribution is more homogeneous in the transverse direction of the strip.An additional transverse compressive stress is created and a buckling is also observed due to the friction during the strip motion in the second step.Once the buckling is appearance,it is very hard to be removed only through decreasing the applied longitudinal tension,because the strip wrinkle still keeps high level due to the effect of the buckled strip,the wrinkle would evolve into buckling eventually.The buckling formation process predicted by the finite element model is very similar to those observed in industrial processing lines.It takes place on the cylindrical part of the tapped roll and the buckling is moving to the middle part of the tapped roll with the increase of the crown,its width is about 2-4 mm.The criterion for the buckle occurrence is also discussed,in the prescribed situation,the transverse shell curvature increases with the strip displacement,if the transverse shell curvature reaches 0.1 mm^(-1), the buckling would take place.

Electromechanical cracking in ferroelectrics driven by large scale domain switching

Experimental results indicate three regimes for cracking in a ferroelectric double cantilever beam (DCB) under combined electromechanical loading. In the loading, the maximum amplitude of the applied electric field reaches almost twice the coercive field of ferroelectrics. Thus, the model of small scale domain switching is not applicable any more, which is dictated only by the singular term of the crack tip field. In the DCB test, a large or global scale domain switching takes place instead, which is driven jointly by both the singular and non-singular terms of the crack-tip electric field. Combining a full field solution with an energy based switching criterion, we obtain the switching zone by the large scale model around the tip of a stationary impermeable crack. It is observed that the switching zone by the large scale model is significantly different from that by the small scale model. According to the large scale switching zone, the switch-induced stress intensity factor (SIF) and the transverse stress (T-stress) are evaluated numerically. Via the SIF and T-stress induced by the combined loading and corresponding criteria, we address the crack initiation and crack growth stability simultaneously. The two theoretical predictions roughly coincide with the experimental observations.