Stress In Thickness Direction Research Articles

Evaluation of Fracture Behavior of Oxide Scale on Carbon Steel Using indentation test and AE Technique

The purpose of this study is to evaluate the fracture behavior and adhesion quality for an oxide scale on low carbon steel with different magnetite and ustyte structure. In this study, samples with different microstructure were prepared under different heat treatment conditions, and an indentation test was performed with AE technique on the oxide scale surface. Cracks were observed at outside of dent area (ring cracks) and in the oxide scale at center of dent area (vertical cracks). The vertical cracks propagated along the grain boundary between magnetite and ustyte. Delamination along the interface between the scale and substrate was also observed as AE signal was detected at last part of un-loading process. In order to estimate the stress distribution under the indentation testing, FEM was performed. Large tensile stress in radius direction was observed at both center and out-side of dent area during loading process. Vertical and ring cracks would be induced by those radius tensile stresses. Large tensile stress in thickness direction was observed at last part of un-loading process and would produce the delamination.

Refined orthotropic beam models based on Castigliano’s theorem and an approximate solution of the compatibility equation

This paper presents an extension of Castigliano’s second theorem for orthotropic beams. The notion “extension” in this context means to find more accurate results not only for the vertical deflection, but also for the horizontal deflection and the rotation angle. For this purpose the Airy stress function is calculated for an orthotropic rectangular strip based on the iterative approximation method from Boley-Tolins when distributed loads or shear tractions are assumed as surface loads. Hence all stress components can be derived from the stress function and may be inserted into the complementary strain energy. Computing the partial derivative of the complementary strain energy with respect to a scalar dummy parameter, the weighted displacement field components over the cross section are obtained. Finally the analytical results from the extended Castigliano theorem (ECT) are verified by two-dimensional (2D) analytical results for an orthotropic cantilever and a clamped-hinged beam and the outcome is also compared to Bernoulli–Euler and to Timoshenko results. The accuracy of the derived results is higher than that derived by the Timoshenko theory because the normal stress in thickness direction is properly taken into account. Moreover it is demonstrated that this lower order normal stress which is caused by distributed loads yields a mean horizontal elongation or shrinkage that is not considered by the Timoshenko beam theory. Hence, highly accurate formulations for laminated composite beams, involving sandwich-structures or multi-layered beams with imperfect bonding, may be derived from the present orthotropic beam model in the future.

Flexoelectric and surface effects on vibration frequencies of annular nanoplate

This research points out the positive results of flexoelectricity and surface effect on the nonlocal vibration of annular nanoplate. First-order shear deformation plate theory is used to formulate the problem. According to the new form of nonlocal elasticity theory, small-scale effects are taken into account. The nanoplate is subjected to a potential electric. The influences of surface stresses and properties including surface residual stresses, surface mass density and surface elasticity are considered. The principle of virtual work is used to derive the governing equations of equilibrium. Finally, differential quadrature method (DQM) in conjunction with the iterative method is utilized to solve equations of motion. Parametric study is done to examine effects of parameters such as radius ratio, nonlocality, thickness-to-radius ratio, different mode numbers, surface properties, normal stress in thickness direction and stretching effect on the size-dependent vibration of flexoelectric nanoplate. The results demonstrate that the consideration of flexoelectric and surface effects leads to significant increase in the natural frequency of flexoelectric nanoplate. The results of this research are utilized in aerospace, military facilities and industries.

Study on machining deformation control of fiber‐metal laminates

AbstractWhen composite products are machined to designed shapes, geometrical deformations are generated with removal of materials, which is caused by release of residual stresses generated during the curing process of composite materials. Due to the uncontrollability of the deformation in machining process, both requirements of form and dimensional tolerances are difficult to meet. Inspired by the relationship between material removal and stress release of the slitting method, a deformation control methodology by introducing stress‐release‐groove in machining process was proposed. Residual stresses were firstly measured by using the slitting method and the distribution of residual stresses in thickness direction was estimated. Finite element model was then created and used to study the influence of machining process on geometrical deformation of the composite. It was found that the pre‐processing grooves can reduce the subsequent processing deformation and consequently improve the machining accuracy. To make the release of stress controllable, the influences of width, spacing, depth, and processing sequence of grooves on machining deformation were numerical studied.

Effect on magnetic properties of inhomogeneous compressive stress in thickness direction of an electrical steel stack

The manufacturing processes of electrical machines may lead to significant degradation of magnetic core properties and therefore of the machine performance. Laminations are usually stacked and pressed which affects the magnetic properties and the iron losses. However, the influence of this step must be still investigated when large generators are considered. Indeed, in that case, the stator and rotor stacking process consists in assembling several stacks of electrical steel sheets separated by airvents. The surface of the airvent spacers represents about ten percent of the lamination surface of the magnetic circuit, implying, during the compaction process, an inhomogeneous stress distribution with significant local stresses. The present work deals with the experimental characterization of a lamination stack, including airvents, under compressive stress in the thickness direction. A mock-up has been designed and built-up to study magnetic properties of lamination stacks under pressing conditions corresponding to the industrial process.

Accurate prediction of springback after coining operation

A common approach used to reduce springback in flanging operations is to apply additional coining around the bent regions. In this strategy, the sheet metal part is compressed between two rigid dies having a clearance less than the sheet thickness. The aim is to bring additional compressive stresses especially around bending dominated regions. These stresses are slightly larger than the current yield stress of the material. By this way, the dominant bending stress state is reduced leading to less springback. The shell elements which are the state of the art in productive utilization of finite element simulations lack the ability to consider normal deformation which occurs during coining. Hence, it is not possible for process planners to decide on the degree of coining and to predict the springback results beforehand. In order to address this problem a set of experiments were performed, whereby deep drawn cups were coined around the punch radius region and cup bottom. To investigate the changed state of residual stresses, drawn cups were cut into halves and springback was measured. The same procedure was also simulated with the new thick shell elements which are improved to incorporate the normal stresses in thickness direction. It was seen that, by the help of this enhancement, the springback prediction is improved as compared to the conventional shell elements.

A layered shell element for the computation of interlaminar shear stresses and thickness normal stresses

AbstractIn this contribution a layered shell element for the computation of laminated structures is proposed. The shell kinematic is based on the Reissner‐Mindlin theory with an inextensible director field. Further a multi‐field functional is introduced including the global shell equations and additional Euler‐Lagrange equations. These Euler‐Lagrange equations enforce the correct shape of warping through the thickness and lead to continuous transverse shear stresses at layer boundaries This leads to a mixed hybrid shell element, after elimination of stresses, warping and Lagrange parameters on element level. The resulting shell element has the usual 5 or 6 degrees of freedom per node, making it possible to apply this element to complex geometrical structures. An extension of the element to compute stresses in thickness direction is shown, in order to estimate and predict interlaminar failure. The computed results show good agreement with 3D solid shell models. Numerical examples for the computation of interlaminar shear and thickness normal stresses are shown and compared to results of 3D elements. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An isogeometric Reissner-Mindlin shell element for dynamic analysis considering geometric and material nonlinearities

The present approach deals with the dynamical analysis of thin structures using an isogeometric Reissner-Mindlin shell formulation. Here, a consistent and a lumped mass matrix are employed for the implicit time integration method. The formulation allows for large displacements and finite rotations. The Rodrigues formula, which incorporates the axial vector is used for the rotational description. It necessitates an interpolation of the director vector in the current configuration. Two concept for the interpolation of the director vector are presented. They are denoted as continuous interpolation method and discrete interpolation method. The shell formulation is based on the assumption of zero stress in thickness direction. In the present formulation an interface to 3D nonlinear material laws is used. It leads to an iterative procedure at each integration point. Here, a J2 plasticity material law is implemented. The suitability of the developed shell formulation for natural frequency analysis is demonstrated in numerical examples. Transient problems undergoing large deformations in combination with nonlinear material behavior are analyzed. The effectiveness, robustness and superior accuracy of the two interpolation methods of the shell director vector are investigated and are compared to numerical reference solutions.

Non-Destructive Residual Stress Analysis of Induction Hardened Components by Neutron and X-Ray Diffraction

In this paper the microstructural and residual-stress analysis of an induction hardened plate of medium carbon steel is described. The stress gradient was determined using laboratory X-ray diffraction (IWT, Bremen, Germany) and neutron strain scanning (ILL, Grenoble, France). Due to slight variations of chemical composition in the depth, matchstick like (cross section 2×2mm²) d0-reference samples were prepared from a similarly treated sample. The d0shift induced by variation of chemical composition was measured by neutron and by X-ray diffraction along the strain free direction (sin²ψ*) and used for the evaluation of the neutron stress calculation. The d0distribution obtained from the neutron measurement did not appear reliable while the method using X-ray diffraction seems to be an efficient and reliable method to determine d0profiles in small samples. The evaluation of neutron measurements was then done using the X-ray diffraction d0distribution. High compressive residual stresses were measured in the hardened layer followed by high tensile residual stresses in the core. A comparison of the neutron measurements with X-ray diffraction (XRD) depth profiles obtained after successive layer removal showed that both methods give similar results. However, these investigations opened the question about the direct comparison of the residual stresses obtained by neutron and XRD. Indeed, a correction of the neutron data regarding the residual stresses in thickness direction might be necessary as these are released in the case of X-ray diffraction measurements after layer removal.

Model-scale ice — Part A: Experiments

This paper is presenting novel model-scale ice property measurements for grain size, elastic strain-modulus, compressive and tensile specimen tests. The testing and analyzing procedure is targeted to define the basic material behavior accurately to understand the material behavior for the future development of a numerical material model. Additionally, the model-scale ice thickness and the bending strength (following ITTC) are determined to classify the ice properties. The experiments consist of systematic in-situ tests to identify the model-scale ice properties in a format suitable for numerical simulations. The elastic strain-modulus is determined on the intact level ice sheet based on the load displacement relationship of the infinite plate deflection. All specimens are cut with a template to minimize dimensional variations. The specimens are loaded with a linear drive at constant speed while displacement and force are recorded. The resulting load–displacement curves indicate good repeatability. The experiments are conducted over a time of 4h–5h in the keeping phase, where the cooling system is adjusted to maintain the mechanical ice properties, and the obtained results do not show a dependency on the time of testing. A linear-elastic finite element model is used to reproduce the plate bending measurements for the elastic strain-modulus determination. Therewith, it is found that the actual elastic strain-modulus is 27% larger than in plain stress theory due to stresses in thickness direction. Additionally, the approximate yield strength of the model-scale ice is investigated and is found to be significantly lower than the determined maximum stresses in compression, tension and bending. Consequently, this paper contributes to a deeper understanding of the mechanics of model-scale ice, and a procedure is shown how the mechanical parameters can be determined by systematic experiments and analyses.

Magnetic Properties of Particular Shape Specimen of Nonoriented Electrical Steel Sheet Under Compressive Stress in Thickness Direction

The issue of design of motor core is that the estimated iron losses and measured ones are sometimes different. One of the causes is the magnetic deterioration of electrical steel sheet by bolt bundles, etc. We measured the magnetic properties when the compressive stress in thickness direction is impressed on the nonoriented electrical steel sheet. In this paper, magnetic properties of ring, semicircular ring, strip of nonoriented electrical steel sheet under the compressive stress in thickness direction are measured. The different behavior of magnetic properties of various specimens are discussed. It is shown that the iron loss of semicircular ring specimen can be reduced under compressive stress.

Microstructure-Based Modeling of Residual Stresses in WC-12Co-Sprayed Coatings

In this study, the residual stresses in a thermal-sprayed tungsten carbide-cobalt coating are numerically investigated after a plasma-spraying process and after a subsequent roller-burnishing process. The results from the simulations are compared to the first experimental results obtained by a classical hole-drilling method. First, effective material parameters are identified by a detailed microstructure FE model based on scanning electron microscope (SEM) images of the coating. Then, two types of simulations are performed with regard to thermally induced residual stresses as well as the rolling process. In the first model, the microstructural details like pores, interface, and surface roughness are modeled in detail based on light microscope (LM) images. In the second model, the coating and substrate are assumed to be ideal homogeneous, and the interface and surface to be as planar. Furthermore, two types of boundary conditions are investigated: (1), the periodic boundary conditions for the left and right faces, and, (2) when these faces are free. It is shown that, for large sample sizes, the results nearly coincide. The simulation results show increasing compressive residual stresses in thickness direction after the rolling process, which is in qualitative agreement with the experiment. A layer of tensile stresses is obtained at the surface in the simulation which could not be captured by the hole-drilling method. Furthermore, an investigation with homogeneous material behavior is performed in 3D.

Effect of Compressive Stress in Thickness Direction on Iron Losses of Nonoriented Electrical Steel Sheet

The electrical steel sheet is widely used in iron cores of motors, etc. The magnetic properties of a motor core are affected by the distortion due to the compressive stress in the thickness direction caused by bolt bundles, etc. There have been few reports of magnetic properties being investigated systematically, although the detailed examination of the behavior of magnetic properties is important for the precise design of motor, etc. In this paper, the correlation between the compressive stress and its magnetic properties of a nonoriented electrical steel sheet is measured, using a single sheet compressed in the thickness direction. Moreover, the behavior of hysteresis loss and the eddy current loss under the compressive stress in the thickness direction is examined.

A New Calculating Model of Rolling Pressure during Temper Rolling Process

A set of new mathematical models have been developed to calculate the temper rolling force of 2050 strip temper rolling mill. Based on the fact of small plastic deformation and elastic deformation occurring on the entry and exit of the deformation zone, new stress boundary conditions are described. The inhomogeneous distribution of internal stress in thickness direction is taken into account in the models, instead of uniform internal stress and assumption of plane strain traditionally. The new mathematical models have been applied into the temper rolling of 2050 hot rolling mills with good results. Comparison of calculated values and testing values for nine typical products has been given. The result shows that the calculated value of rolling force of temper mill is accurate.

Rapid change of stresses in thickness direction in long orthotropic tube under internal pressure and axial load

Exact solution for long orthotropic tube under internal pressure and axial load suggests the existence of very dangerous combinations of elastic properties. We demonstrate that such elastic properties can be thermodynamically stable. Close to a dangerous combination, stress components change very rapidly in radial direction, resulting in huge peak stresses exceeding the membrane theory predictions by several orders of magnitude, even for relatively thin-walled tubes. Another manifestation of this effect is extreme sensitivity of peak stresses to variations in elastic properties. Away from the critical condition the anomaly in stress distribution disappears and this can be the key point in the design of related structures. The rapid change of stresses in thickness direction is attributed to the auxetic property (negative Poisson’s ratio) of highly anisotropic material of the tube. As an example, we consider the filament wound tube with closed ends under internal pressure and demonstrate that, for highly anisotropic fiber-reinforced plastic, winding with angle close to 45° is potentially dangerous.

Temperature and stress fields of multi-track laser cladding

Based on genetic algorithm and neural network algorithm, the finite element analyses on the temperature fields and stress fields of multi-track laser cladding were carried out by using the ANSYS software. The results show that, in the multi-track cladding process, the temperature field ellipse leans to the cladding formed, and the front cladding has preheating function on the following cladding. During cladding, the longitudinal stress is the largest, the lateral stress is the second, and the thickness direction stress is the smallest. The center of the cladding is in the tensile stress condition. The longitudinal tensile stress is higher than the lateral or thickness direction stress by several times, and the tensile stress achieves the maximum at the area of joint between the cladding and substrate. Therefore, it is inferred that transversal crack is the most main crack form in multi-track laser cladding. Moreover, the joint between cladding and substrate is the crack sensitive area, and this is consistent with the actual experiments.

厚板冷間ロール矯正工程のオンライン残留応力の予測モデル開発

An on-line model predicting the residual stress in roller leveling process is developed. In order to simplify the formulation, the plain strain (dεz=0) condition is assumed and the stress in thickness direction is ignored (σy=dσy=0). The camber and gutter deformation of the real sized plate are measured and compared with the prediction values of the model to validate the accuracy of the model. The variations of residual stress are studied according to the entry and the delivery intermeshes, respectively. The camber deformation decreases linearly as increasing the entry intermesh. But the gutter deformation does not vary directly as the intermesh. Therefore, the optimum intermesh values should be found to minimize both the camber and the gutter deformation.

Automatic adaptation of an integration formula in thickness direction for solid‐shell elements

AbstractIn the simulation of shell problems in which plastic stresses in thickness direction are developed, the necessity of a more accurate integration through thickness using more integration points e.g. Gauss points becomes obvious, often increasing respectively the computational time and effort. A new algorithm is proposed for the automatic adaptation of the integration formula in thickness direction during the computation. Simple engineering criteria are found to define the time‐point and the regions to increase the number of integration points. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

407 Cross-Ply CFRP積層板の高サイクル疲労におけるトランスバースクラック及び層間はく離進展挙動の調査(高分子/高分子基複合材料1)

Damage growth behavior of transverse crack and delamination in cyclic loading was studied with cross-ply laminates of carbon fiber reinforced plastics (CFRPs) composite. Damage of the specimens during the fatigue test was observed by soft X-ray photography. It was found that delamination growth behavior depended on the inter-laminer stress and the out-plane stress in thickness direction caused by free-edge effect. Quasi-isotropic, [45/0/-45/90]_s, laminates, are applied large peering stress at free edges of the specimen when the specimen is subjected to tensile stress. Therefore they showed edge delamination. On the other hands, cross-ply, [0/90_6]_s laminates, are applied large inter-laminer shear stress at transverse crack tips, and show local delamination originated by a transverse crack. Under the high-cycle loading, it was observed that depending on the applied stress level delamination growth behavior differed.

On consistent plate theories

Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction.