Overview on the Prediction Models for Sheet Metal Forming Failure:Necking and Ductile Fracture

The formability of the material determines the amount of available deformation before failure and thus is important for the production of various structural components in industries. The workability of materials is commonly evaluated by different forms of failure models during sheet metal forming(SMF) processes. In order to provide a whole picture about the prediction models for SMF failure, necking-related formability and ductile fracture-related formability studies in SMF processes are systematically summarized, the applicability and limitation of each model are highlighted, and the link between forming limit diagram and ductile fracture criterion is pointed out. Conclusions about some critical issues on failure in SMF are made.     

Out-of-plane Testing Procedure for Inverse Identification Purpose: Application in Sheet Metal Plasticity

Many recent works in inverse identification of constitutive parameters have pointed to the need of tests which exhibit heterogeneous strain paths. The present study details a new testing procedure based on out-of-plane motion capture by Stereo-Image Correlation (SIC). With the original test proposed hereby, a unique sample is deformed on a tensile machine along two perpendicular tensile directions, two perpendicular shear directions and one expansion area. The choice of the sample shape is discussed along with the stereo imaging device, 3D reconstruction and measurement uncertainties. The test sample is made from a sheet of commercially pure titanium. A Finite-Element updating inverse method is applied in order to identify six parameters of an anisotropic plastic constitutive model. Results show that this new testing procedure allows every constitutive parameter of the model to be identified from one and only one test.     

Inferring Post-Necking Strain Hardening Behavior of Sheets by a Combination of Continuous Bending Under Tension Testing and Finite Element Modeling

Experimental Mechanics - This paper presents a combined experimental and simulation approach to identify post-necking hardening behavior of ductile sheet metal. The method is based on matching a...     

FAST ACCURATE PREDICTION OF BLANK SHAPE IN SHEET METAL FORMING

By using the Finite Element Inverse Approach based on the Hill quadratic anisotrop-ically yield criterion and the quadrilateral element, a fast analyzing software-FASTAMP for the sheet metal forming is developed. The blank shapes of three typical stampings are simulated and compared with numerical results given by the AUTOFORM software and experimental results, respectively. The comparison shows that the FASTAMP can predict blank shape and strain distribution of the stamping more precisely and quickly than those given by the traditional methods and the AUTOFORM.     

Large Strain Shear Compression Test of Sheet Metal Specimens

A hybrid experimental-computational procedure to establish accurate true stress-plastic strain curve of sheet metal specimen covering the large plastic strain region using shear compression test data is described. A new shear compression jig assembly with a machined gage slot inclined at 35° to the horizontal plane of the assembly is designed and fabricated. The novel design of the shear compression jig assembly fulfills the requirement to maintain a uniform volume of yielded material with characteristic maximum plastic strain level across the gage region of the Shear Compression Metal Sheet (SCMS) specimen. The approach relies on a one-to-one correlation between measured global load–displacement response of the shear compression jig assembly with SCMS specimen to the local stress-plastic strain behavior of the material. Such correlations have been demonstrated using finite element (FE) simulation of the shear compression test. Coefficients of the proposed correlations and their dependency on relative plastic modulus were determined. The procedure has been established for materials with relative plastic modulus in the range 5?×?10^?4?<?(E _p /E)?<?0.01. It can be readily extended to materials with relative plastic modulus values beyond the range considered in this study. Nonlinear characteristic hardening of the material could be established through piecewise linear consideration of the measured load–displacement curve. Validity of the procedure is established by close comparison of measured and FE-predicted load–displacement curve when the provisional hardening curve is employed as input material data in the simulation. The procedure has successfully been demonstrated in establishing the true stress-plastic strain curve of a demonstrator 0.0627C steel SCMS specimen to a plastic strain level of 49.2 pct.     

Anisotropic Hardening of Sheet Metals at Elevated Temperature: Tension-Compressions Test Development and Validation

New test equipment has been developed to measure the in-plane cyclic behavior of sheet metals at elevated temperatures. The tester has clamping dies with adjustable side force to prevent the sheet specimens from buckling during compressive loading. In addition to the room temperature experiment, cartridge type heaters are inserted in the clamping dies so that the specimen can be heated up to 400 °C during the cyclic tests. For the strain measurement, a non-contact type laser extensometer is used. In order to validate the newly developed test device, the tension-compression (and compression-tension) tests under pre-strains and various temperatures have been performed. As model materials, the aluminum alloy sheet which exhibits a large Bauschinger effect and the magnesium alloy sheet which exhibits different amounts of asymmetry under cyclic loading are used. The developed device can be well-suited to measure the cyclic material behavior, especially the anisotropic and asymmetric hardening of light-weight materials.     

Multi-Axial Deformation Setup for Microscopic Testing of Sheet Metal to Fracture

While the industrial interest in sheet metal with improved specific-properties led to the design of new alloys with complex microstructures, predicting their safe forming limits and understanding their microstructural deformation mechanisms remain as significant challenges largely due to the inadequacy of the existing experimental tools. The investigation of the strain-path dependent failure mechanisms requires miniaturized testing equipment, which can be placed in a scanning electron microscope for in situ experiments. So far, such tests could only be carried out for a single strain path (uniaxial tension). In this work, in order to fill this gap, a miniaturized Marciniak test setup is designed, built and tested. With this setup real-time, multi-axial tests of industrial sheet metal can be carried out to the point of fracture within a scanning electron microscope. Proof-of-principle experiments demonstrate that a realm of information can be obtained, crucial for the understanding of the mechanical behavior of new alloys.     

板料三维成形过程的有限元数值模拟

基于有限变形理论建立了三维金属板料成形过程的刚塑性有限元数学模拟,该数学模型采用物质坐标系中的Ｕｐｄａｔｅ－Ｌａｇｒａｎｇｅ描述,等向强化假设,考虑了板料的厚向异性,对于金属板料与模具有摩擦采用近似的库仑摩擦定律以改善计算的收敛性。为简经计算采用薄膜单元,并根据此模型编制程序。     

Hardening of an elastoplastic body

The purpose of the experimental investigations whose results are described here is to study plastic states in which loading occurs in some directions and unloading in others, and also to verify the applicability of the plastic strain schemes proposed in [1,2] for these states. The existence of an angular point on the loading surface is detected. The influence of the loading path on the development of this point is investigated. A load of biaxial tension type was produced in a 45KhN steel-pipe specimen subjected to internal pressure and an axial force. The ratio between the principal stresses hence varied, but the principal directions of the stress tensor remained fixed in the body of the specimen.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 144–148, May–June, 1976.The author is grateful to E. I. Shemyakin for supervising the research, and to V. M. Zhigalkin, G. F. Bobrov, and N. S. Adigamov for taking part in performing the tests.     

Erosion of Ductile and Brittle Materials

The fundamental mechanisms of erosion by solid particle impact were investigated in both brittle and ductile materials. A review of the literature of erosion theoretical models indicated various different models. The most important ones were used to reproduce experimental tests concerning the erosion by solid particle impingement using gas jets. If supported by an appropriate tuning of certain parameters, they perform well. Since a continuous tuning of these parameters is required, experiment based theoretical models seem to be inappropriate in the development of advanced materials for high temperature applications. Consequently, we have developed a new approach based on the finite element method. Since it only requires the knowledge of the main mechanical properties as a function of the temperature, it seems suitable for the erosion rate evaluation in a wide range of applications. Early assessment results, compared to experimental erosion tests conducted at room temperature, showed good predictive capabilities which are even better than theoretical models.     

延性动态损伤的细观描述

对动载荷下材料的延性动态损伤的细观力学研究现状进行了评述，详细讨论了现有的几类典型的动态延性损伤的微孔生长模型。针对目前该领域工作中存在的问题，指出了今后应开展的工作方向。     

Dissipation-Induced Instability Phenomena in Infinite-Dimensional Systems

This paper develops a rigorous notion of dissipation-induced instability in infinite dimensions as an extension of the classical concept implicitly introduced by Thomson and Tait for finite degree of freedom mechanical systems over a century ago. Here we restrict ourselves to a particular form of infinite-dimensional systems—partial differential equations—whose inherent function-analytic differences from finite-dimensional systems make uncovering this notion more intricate. In building the concept of dissipation-induced instability in infinite dimensions we found Arnold’s and Yudovich’s nonlinear stability methods, for conservative and dissipative systems respectively, along with some new existence theory for solutions, to be the essential foundation. However, when proving the results for classical solutions, as motivated by their direct physical significance, we had to overcome a number of fundamental difficulties associated with existing stability analysis methods, which has led to new techniques. In particular, in this work we establish the connection of existence and general stability theories in strong and weak topologies and provide new insights into the physics and geometry of the dissipation-induced instability phenomena in infinite-dimensional systems. As a paradigm and the first infinite-dimensional example to be rigorously analyzed, we use a two-layer quasi-geostrophic beta-plane model, which describes the fundamental baroclinic instability in atmospheric and ocean dynamics; early formal linear approximate studies suggested that this system can be destabilized after the introduction of dissipation.     

Ductile versus brittle behavior of amorphous metals

Ductile behavior of amorphous metals, their ability to sustain localized flow at high nominal stresses, is attributed to a mechanism which alleviates the severe stress conditions prevailing near potential cleavage flaws. The model problem of the plane strain deformation of an infinite block of non-linear visco-elastic material containing an elliptical hole is studied numerically and analytically. A strong dependence of the viscosity on the hydrostatic tension, a result of the increase in the number of viscous flow defects with dilatation, is the principal source of non-linearity. The analysis reveals that, under a constant remote strainrate, the initial elastic stress distribution ahead of the hole gives way, with time, to a more uniform stress distribution. Altering the stress distribution permits the remote (nominal) stress to achieve higher values before critical stress conditions are reached locally at the concentrator. At ordinary temperatures, amorphous metals are not in thermodynamic equilibrium; this motivates a modification of the constitutive law that reflects the kinetic difficulty of maintaining thermodynamic equilibrium under conditions of varying hydrostatic tension. Re-solving the elliptical hole problem with the modified constitutive law reveals a delay in the stress redistribution in front of the concentrator which may explain brittle fracture.     

Ductile reinforcements for enhancing fracture resistance in composite materials

Ductile reinforcements can supply fracture toughness to a polymer matrix by pulling out and by plastically deforming. In the case of metal reinforcements that are not in a toughened condition, there may be more toughening to be gained when the fibers remain in the matrix and plastically deform rather than pulling out. These fibers can be said to have an unused plastic potential. When these fibers bridge a crack, their plastic deformation causes a rise in the force which is trying to pull out the fiber. Because of this, the shape of the fiber must be adjusted along its length if it is to remain anchored and contribute its plastic work. The use of anchored, ductile fibers provides a new design axis that brings new possibilities not achievable by the current research focus on the fiber–matrix interface. This paper describes the experimental pullout of aligned ductile fibers from a polymer matrix, and indicates the effect of the shape and embedded length of the fiber on the toughness increase of the composite. Anchored, plastically deforming fibers are shown to provide a major improvement to the toughening. Even for unoptimized ductile fibers, the calculated toughening improvement equals or exceeds the toughening available from current short glass or graphite fibers. In addition, pullout values are obtained for fibers that are embedded at an angle, simulating fiber bridging from fibers not perpendicular to the crack surface. These results further demonstrate the toughening efficiency of ductile fibers.     

Localization Phenomena in Liquid-Saturatedand Empty Porous Solids

Localization phenomena occur as a result of local concentrations of plastic deformations in small bands of finite width (shear bands). Porous materials, as, for instance, soil, rock, concrete and sinter materials as well as polymeric and metallic foams exhibit a strong tendency towards shear banding caused by plastic dilatation in the brittle deformation range. This kind of behaviour is of great practical importance in engineering design, for example in the study and computation of failure mechanisms in soil mechanics (base failure, slope failure, etc.). From the mathematical point of view, the computation of localization phenomena, for example within the framework of the finite element method (FEM), yields an ill-posed problem, since each mesh refinement leads to smaller shear bands until one obtains (ideally) a singular surface. Following this, regularization mechanisms should be introduced to obtain reliable and robust results.In the present article, two natural regularization mechanisms for liquid-saturated and empty granular porous materials are discussed. These mechanisms are (1) the inclusion of additional independent degrees of freedom in the sense of the Cosserat brothers for the granular porous solid and (2) the inclusion of pore-fluid viscosity in the saturated case.     

Frictional Phenomena in Dynamical Systemwith Two-Frequency Excitation

The paper deals with investigation of a self-excited vibrating system with dry friction. The system is composed of a mass connected by viscoelastic element with the referring frame and interacting with a moving belt by means of dry friction. An experimentally identified, multi-parametric dry friction model for the pair composed of soft and hard elements like steel–polyester pair, describing both the case of stick-slip and quasi-harmonic vibration, has been applied. Additionally, the system is influenced by external, two-frequency kinematic excitation. The results of computer simulation for different excitation conditions are submitted in the present paper.     

Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing

We derive optimal scaling laws for the macroscopic fracture energy of polymers failing by crazing. We assume that the effective deformation-theoretical free-energy density is additive in the first and fractional deformation-gradients, with zero growth in the former and linear growth in the latter. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. For this particular geometry, we derive optimal scaling laws for the dependence of the specific fracture energy on cross-sectional area, micromechanical parameters, opening displacement and intrinsic length of the material. In particular, the upper bound is obtained by means of a construction of the crazing type.     

Discrete Homogenization in Graphene Sheet Modeling

Graphene sheets can be considered as lattices consisting of atoms and of interatomic bonds. Their bond lengths are smaller than one nanometer. Simple models describe their behavior by an energy that takes into account both the interatomic lengths and the angles between bonds. We make use of their periodic structure and we construct an equivalent macroscopic model by means of a discrete homogenization technique. Large three-dimensional deformations of graphene sheets are thus governed by a membrane model whose constitutive law is implicit. By linearizing around a prestressed configuration, we obtain linear membrane models that are valid for small displacements and whose constitutive laws are explicit. When restricting to two-dimensional deformations, we can linearize around a rest configuration and we provide explicit macroscopical mechanical constants expressed in terms of the interatomic tension and bending stiffnesses.     

锅炉用钢材强化规律的实验研究

通过对六种锅炉用钢材的实验研究,得到了材料屈服的一些特点,给出了在沿一定加载路径的拉压循环载荷作用下材料的强化规律,以及在拉伸和压缩时材料所表现出的不同性质。     

Hardening evolution of AZ31B Mg sheet

The monotonic and cyclic mechanical behavior of O-temper AZ31B Mg sheet was measured in large-strain tension/compression and simple shear. Metallography, acoustic emission (AE), and texture measurements revealed twinning during in-plane compression and untwinning upon subsequent tension, producing asymmetric yield and hardening evolution. A working model of deformation mechanisms consistent with the results and with the literature was constructed on the basis of predominantly basal slip for initial tension, twinning for initial compression, and untwinning for tension following compression. The activation stress for twinning is larger than that for untwinning, presumably because of the need for nucleation. Increased accumulated hardening increases the twin nucleation stress, but has little effect on the untwinning stress. Multiple-cycle deformation tends to saturate, with larger strain cycles saturating more slowly. A novel analysis based on saturated cycling was used to estimate the relative magnitude of hardening effects related to twinning. For a 4% strain range, the obstacle strength of twins to slip is 3 MPa, approximately 1/3 the magnitude of textural hardening caused by twin formation (10 MPa). The difference in activation stress of twinning versus untwinning (11 MPa) is of the same magnitude as textural hardening.