Deformation and the strip necking zone in a cracked steel sheet

When a tensile stress is applied to a thin cracked plate, a strip necking region results ahead of a crack tip. The relative opening displacement between the crack surfaces and between the upper and lower boundaries of the strip necking region were measured by the moiré method. The strains ahead of the strip necking region and the thickness reduction (therein) were also measured. The measured relative opening displacements were compared with the calculated values using the Dugdale strip necking model. The thickness reduction in the strip necking region is equal to the relative opening displacement.     

The determination of stress and strain concentrations at an ellipsoidal inclusion in an anisotropic material

The aim of this paper is to produce elementary yet explicit formulae for the evaluation of stress and strain concentration factors at an ellipsoidal inclusion, for arbitrary anisotropy, under uniform loading at infinity. The results are such that the required formulae do not involve the solution of any boundary value prolems or the knowledge of any Green's functions. An important feature of the analysis is that the solution of the interface problem is intimately related to the solution of the inclusion problem.     

Determination of tensile flow stress beyond necking at very high strain rate

The objective of this effort was to extend the Bridgman analysis of tensile necking to obtain stress-strain data beyond the point of onset of necking from a split Hopkinson bar. For this purpose, combined analytical and experimental techniques were considered. The analytical efforts were focused on validating the use of Bridgman solutions for high rate of deformation through a finite-element analysis of a tapered tensile specimen. The experimental technique involved the development of a photographic system using a light-emitting diode and a 35-mm rotating drum camera for the observation of necking during dynamic tensile tests conducted with a split Hopkinson tension bar. The developed new technique was successfully used to measure neck profiles of 6061-T6 aluminum, HY100 and 1020 steel tensile specimens. The measured profiles were used with the Bridgman analysis and stress-strain data were obtained to over 70-percent strain.     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

Spatially resolved piezo-spectroscopic characterizations for the validation of theoretical models of notch-root stress fields in ceramic materials

The main aim of this work is a precise experimental assessment of the local stress fields developed at the notch-root in a ruby crystal, selected as a paradigm brittle material, by means of photo- and electron-stimulated luminescence techniques. Our approach takes advantage of the piezo-spectroscopic (PS) effect, which consists of a spectral shift of the luminescence emitted by the material due to lattice strain. Highly spatially resolved stress maps were extensively collected at the notch-root and spectral shifts monitored for the chromophoric (R-lines) fluorescence observed in a single-crystalline ruby sample. Experimental data were analyzed and compared to the theoretical solutions of notch-root stress fields given by Filippi and by Creager-Paris. Due to its inherent simplifications, the Creager–Paris solution was found leading to underestimation of the maximum stress value piled up in the material, while the Filippi’s solution represented a more suitable approximation for the stress field developed at the notch-root.     

Crack-tip fields for fast fracture of an elastic-plastic material

An asymptotic analysis of the near-tip fields is given for transient crack propagation in an elastic-plastic material. The material is characterized by J₂ flow theory together with a bilinear effective stress-strain curve. Both plane stress and plane strain conditions have been considered. Explicit results are given for the order of the crack-tip singularity, the angular position at which unloading occurs, and the angular variation of the near-tip stresses, all as functions of the crack-tip speed and the ratio of the slopes of the two portions of the bilinear stress-strain relation. It was found that the results are much more sensitive to the elastic-plastic constitutive relation than to the crack speed. This result is important for numerical analyses of dynamic crack propagation problems.     

Local solution of the stress and strain fields in the necking section of cylindrical bars under uniaxial tension

The problem of finding the stress and strain fields over the minimum cross section of necked cylindrical bars under uniaxial tensile load has been solved locally using a new fast numerical method. The scheme delivers both the accuracy of the finite element analysis and the applicability of simple closed-form analytical solutions. The required inputs are the distributions of curvature radii for both isostatic and material lines. It is numerically observed that the mathematical formulas available in the literature fail to adequately predict these distributions. Introducing the stress normalized strain-hardening rate as the most decisive parameter affecting the curvature radii, a database and interpolation technique have been developed in order to estimate the necessary information based on the results of the previously FE analyzed samples. Finally, a practical case has been solved and compared with the FE results.     

Numerical analysis of diffuse and localized necking in orthotropic sheet metals

In the present paper the diffuse and localized necking models according to Swift [Swift, H.W., 1952. Plastic instability under plane stress, Journal of the Mechanics and Physics of Solids, 11–18], Hill [Hill, R., 1952. On discontinuous plastic states, with special reference to localized necking in thin sheets. Journal of the Mechanics and Physics of Solids 1, 19–30] and Marciniak and Kuczyński [Marciniak, Z., Kuczyński, K., 1967. Limit strains in the process of stretch-forming sheet metal. International Journal of Mechanical Sciences 9, 609–620], respectively, are considered. A theoretical framework for the mentioned models is proposed that covers rigid–plastic as well as elastic–plastic constitutive modelling using various advanced phenomenological yield functions that are able to account very accurately for plastic anisotropy. The mentioned necking models are applied to different orthotropic sheet metals in order to assess their predictive capabilities and to stress out some potential sources for discrepancies between simulations and experiments. In particular, the impact of the applied hardening curve and the equibiaxial r-value, which was recently introduced by Barlat [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Choi, S.-H., Pourboghrat, F., Chu, E., Lege, D.J., 2003. Plane stress yield function for aluminium alloy sheets – part 1: theory. International Journal of Plasticity 19, 297–1319], on formability prediction is investigated. Furthermore, the impact of the Portevin–LeChatelier effect on the formability of aluminum sheet metals is discussed.     

Continuous, large strain, tension/compression testing of sheet material

Modeling sheet metal forming operations requires understanding of the plastic behavior of sheet alloys along non-proportional strain paths. Measurement of hardening under reversed uniaxial loading is of particular interest because of its simplicity of interpretation and its application to material elements drawn over a die radius. However, the compressive strain range attainable with conventional tests of this type is severely limited by buckling. A new method has been developed and optimized employing a simple device, a special specimen geometry, and corrections for friction and off-axis loading. Continuous strain reversal tests have been carried out to compressive strains greater than 0.20 following the guidelines provided for optimizing the test. The breadth of application of the technique has been demonstrated by preliminary tests to reveal the nature of the Bauschinger effect, room-temperature creep, and anelasticity after strain reversals in commercial sheet alloys.     

On the implementation of anisotropic yield functions into finite strain problems of sheet metal forming

In this article the implementation of anisotropic yield functions into finite element investigations of orthotropic sheets with planar anisotropy is discussed within a plane-stress context. Special attention is focused on the proper treatment of the orientation of the anisotropic axes during deformation into the finite-strain range. As an example problem the hydrostatic bulging of a membrane is considered in conjunction with a recently proposed anisotropic yield function. It is shown that the aspects of the plane-stress assumption, which do not come into consideration in isotropic analyses, can play an important role on the accuracy of the solution when the rotation of the orthotropic axes enters the computation directly due to the presence of material anisotropy. When the material anisotropy is considered and when the deformation of the workpiece is not limited to the plane of the undeformed sheet (such as cup drawing, hydrostatic bulging, etc.), the numerical experiments indicate that the only correct formulation is the one based on numerically imposing the requirement that for the plane-stress application, the in-plane material axes have to remain in the plane of the sheet during the deformation.     

Prediction of elastic strain recovery of a formed steel sheet considering stiffness degradation

The aim of this work is to show first, how the springback of a steel sheet drawn part is affected by the stiffness degradation, as it results from the damage evolved during forming process, and second, to build a respective modeling approach to take this degradation into account. For the consideration of the orthotropic elastic properties degradation we develop an approach, based on the Mori-Tanaka theory, where damage is considered by inclusion of ellipsoidal cavities. The respective void shape evolution is proposed to be identified with the measurements of elastic modulus in two perpendicular directions during the uniaxial tensile test of a flat specimen at different loading stages. The proposed approach is coupled with the Gurson-Tvergaard-Needleman (GTN) plastic potential, though it could be substituted by almost any other continuum damage model. At the end the presented approach is experimentally validated by a simple springback test, developed by authors. A very good agreement between by calculation predicted and measured springback amount is observed.     

Numerical analysis of fast fracture and crack arrest in a sheet of elastic perfectly-plastic material

The dynamic fields for acceleration, deceleration and arrest of a crack tip have been investigated numerically. We consider cracks which start to extend rapidly under brittle conditions. The crack-tips then enter regions of elasto-plastic constitutive behavior and they are subsequently arrested. Results have been obtained for a symmetrically expanding central crack and for an edge crack, both in thin sheets. The elasto-plastic behavior has been described by J₂ flow theory, with the von Mises yield criterion and a bilinear relation between effective stress and effective strain. Numerical results are presented for stress and strain components at a short distance ahead of the propagating and arresting crack tips.     

拉伸应变率对20钢层裂特性的影响

采用轻气炮加载技术和激光速度干涉(VISAR)测速技术相结合,对不同拉伸应变率条件下20钢的层裂特性进行了实验研究。通过改变飞片和样品的几何尺寸来调整拉伸应变率的大小,研究了拉伸应变率对20钢层裂强度的影响。实验的拉伸应变率的变化范围为104~106 s-1,最大拉伸应变率接近激光加载所能产生的拉伸应变率,相比激光加载,薄飞片技术容易保证一维应变条件。实验结果显示20钢的层裂特性明显依赖着拉伸应变率的大小,106 s-1条件下层裂强度比104 s-1时提高近70%。基于对数值计算结果的分析,讨论了影响层裂强度的主要外载荷因素。     

Effects of spatial grain orientation distribution and initial surface topography on sheet metal necking

The finite element method is used to numerically simulate localized necking in AA6111-T4 under stretching. The measured EBSD data (grain orientations and their spatial distributions) are directly incorporated into the finite element model and the constitutive response at an integration point is described by the single crystal plasticity theory. We assume that localized necking is associated with surface instability, the onset of unstable growth in surface roughening. It is demonstrated that such a surface instability/necking is the natural outcome of the present approach, and the artificial initial imperfection necessitated by the macroscopic M–K approach [Marciniak and Kuczynski (1967). Int. J. Mech. Sci. 9, 609–620] is not relevant in the present analysis. The effects of spatial orientation distribution, material strain rate sensitivity, texture evolution, and initial surface topography on necking are discussed. It is found that localized necking depends strongly on both the initial texture and its spatial orientation distribution. It is also demonstrated that the initial surface topography has only a small influence on necking.     

Stress and strain fields in rotating elastic/plastic annular disks of pressure-dependent material

The Drucker–Prager yield criterion is used in conjunction with its associated flow rule to find the elastic/plastic stress and strain distributions within the rotating annular disks under plane stress conditions. The main distinguished feature of the model, as compared to typical models used for analysis of disks, is that the material is plastically compressible. Using an approach proposed elsewhere, the solution for strain rates is reduced to one nonlinear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one, which significantly simplifies the numerical treatment and increases the accuracy of solution.     

On the modelling of anisotropic elastic and inelastic material behaviour at large deformation

The purpose of this work is the formulation and discussion of an approach to the modelling of anisotropic elastic and inelastic material behaviour at large deformation. This is done in the framework of a thermodynamic, internal-variable-based formulation for such a behaviour. In particular, the formulation pursued here is based on a model for plastic or inelastic deformation as a transformation of local reference configuration for each material element. This represents a slight generalization of its modelling as an elastic material isomorphism pursued in earlier work, allowing one in particular to incorporate the effects of isotropic continuum damage directly into the formulation. As for the remaining deformation- and stress-like internal variables of the formulation, these are modelled in a fashion formally analogous to so-called structure tensors. On this basis, it is shown in particular that, while neither the Mandel nor back stress is generally so, the stress measure thermodynamically conjugate to the plastic “velocity gradient”, containing the difference of these two stress measures, is always symmetric with respect to the Euclidean metric, i.e., even in the case of classical or induced anisotropic elastic or inelastic material behaviour. Further, in the context of the assumption that the intermediate configuration is materially uniform, it is shown that the stress measure thermodynamically conjugate to the plastic velocity gradient is directly related to the Eshelby stress. Finally, the approach is applied to the formulation of metal plasticity with isotropic kinematic hardening.     

Time resolved PIV and flow visualization of 3D sheet cavitation

Time-resolved PIV was applied to study fully developed sheet cavitation on a hydrofoil with a spanwise varying angle of attack. The hydrofoil was designed to have a three-dimensional cavitation pattern closely related to propeller cavitation, studied for its adverse effects as vibration, noise, and erosion production. For the PIV measurements, fluorescent tracer particles were applied in combination with an optical filter, in order to remove the reflections of the laser lightsheet by the cavitation. An adaptive mask was developed to find the interface between the vapor and liquid phase. The velocity at the interface of the cavity was found to be very close to the velocity predicted by a simple streamline model. For a visualization of the global flow dynamics, the laser beam was expanded and used to illuminate the entire hydrofoil and cavitation structure. The time-resolved recordings reveal the growth of the attached cavity and the cloud shedding. Our investigation proves the viability of accurate PIV measurements around developed sheet cavitation. The presented results will further be made available as a benchmark for the validation of numerical simulations of this complicated flow.     

淬硬45钢在高温、高应变率下的动态力学性能及本构关系

在20℃~800℃的温度范围和10-3~104s-1的应变率范围内,采用电子万能试验机和分离式霍 普金森压杆,对淬硬45钢(45HRC)分别进行准静态实验和动态压缩力学性能实验,得到应力应变曲线。结 果表明:淬硬45钢的流动应力对应变率敏感性一般,但表现出较强的温度敏感性,随着应变率的增大而增大, 随着温度的升高而降低。采用以高斯函数表示温度效应的改进Johnson-Cook本构方程拟合了淬硬45钢在 高应变率和高温条件下的本构关系,拟合曲线与实验数据吻合较好。