A hybrid method for detecting the onset of local necking by monitoring the bulge forming load

Strain-based Forming Limit Diagrams (FLD), which are typically obtained under linear or quasi-linear loading conditions, describe the limiting strains in terms of the major and minor in-plane strains before the onset of necking or the final failure (FFD). These strains can be detected by analysing the strain field in the vicinity of necking or cracking defects. It has generally been agreed that the loading versus time signal is not suitable for detecting necking processes. A novel hybrid method of detecting the onset of necking based on the experimental and simulated bulging load is presented in this paper. This method consists mainly in comparing the experimental forming load, i.e., a load showing plastic instability, with the numerical predictions obtained by performing finite element simulation. The simulation of the bulging process does not include any damage or failure criteria. A homogeneous forming load can therefore be simulated without requiring any information about the localization. This method was applied to detecting the onset of local necking in circular and elliptic quasistatic bulge tests on sheet material, with a diameter of 200 mm. Two materials were tested, a 0.8 mm thick DP450 Dual Phase steel sheet and a 1 mm thick AA6016-T4 aluminium sheet. The onset of necking observed with our method was compared with the results obtained by performing Hogström’s analysis based on the measured strain field over time and similar necking strains were obtained. Beside, the Bressian Williams Hill (BWH) shear criterion was identified for each test from experimental results. A slight scattering of the shear stress values was observed.     

Stress based prediction of formability and failure in incremental sheet forming

A strain-based forming limit criterion is widely used in sheet-metal forming industry to predict necking. However, this criterion is usually valid when the strain path is linear throughout the deformation process [1]. Strain path in incremental sheet forming is often found to be severely nonlinear throughout the deformation history. Therefore, the practice of using a strain-based forming limit criterion often leads to erroneous assessments of formability and failure prediction. On the other hands, stress-based forming limit is insensitive against any changes in the strain path and hence it is first used to model the necking limit in incremental sheet forming. The stress-based forming limit is also combined with the fracture limit based on maximum shear stress criterion to show necking and fracture together. A derivation for a general mapping method from strain-based FLC to stress-based FLC using a non-quadratic yield function has been made. Simulation model is evaluated for a single point incremental forming using AA 6022-T43, and checked the accuracy against experiments. By using the path-independent necking and fracture limits, it is able to explain the deformation mechanism successfully in incremental sheet forming. The proposed model has given a good scientific basis for the development of ISF under nonlinear strain path and its usability over conventional sheet forming process as well.     

Numerical study of superplastic deformation with superimposed pressure for cavity sensitive materials

Abstract

The non-uniform deformation (necking and thinning) development and fracture of superplastic materials under both uniaxial tension and circular sheet bulging are numerically analysed by considering the effects of strain rate sensitivity and cavity growth with superimposed pressure. It is found that the fracture mode, which is controlled by both strain rate sensitivity and cavity growth rate, can be changed by superimposed pressure from fracture without external necking for cavity sensitive alloys at zero pressure to fracture with necking development or extensive thinning at pressure large enough to completely suppress cavity growth. Fracture mechanism diagrams are presented which enable prediction of the fracture mode to be made as a function of material parameters and pressure conditions for uniaxial tension and bulging.

MST/724     

A Closer Look at the Diffuse and Localised Necking of A Metallic Thin Sheet: Evolution of the Two Bands Pattern

Plastic strain localisation in a sheet specimen was monitored by electronic speckle pattern interferometry during uniaxial tensile tests. The experiments were carried on in the diffuse and localised necking stages until fracture. A kinematic model, which is independent of material characteristics, was used to describe the whole strain rate field with two crossing localisation bands inclined with respect to the tensile direction. Then, the physical features of localisation, such as the width of the two bands, their inclination angles and their maximum strain rates are identified by least‐square from the displacements fields and their evolutions are followed from the onset of diffuse necking up to the failure. In particular, the effect of the average strain rate is considered and bandwidth evolution is analysed in detail. It was found that:

• The band structure appears early, as soon as diffuse necking starts;
• The separation, in terms of strain rate or bandwidth, of the two bands corresponds to the transition between diffuse and localised necking. The localised necking stage can be divided into two sub‐stages: in the first one, the two bands continue to evolve but at different rates, and in the second one, one of the bands stabilises. The transition between the two sub‐stages is influenced by the crossbeam velocity;
• The inclination of the band leading to fracture remains quite stable, while the other rotates towards a situation perpendicular to the tensile direction;
• The band width decreases exponentially versus the maximum local strain. The two bands follow the same evolution path, but one of them progressively lags behind the other until it stops deforming.
• Although the average strain rate was only varied by a factor two, it was found that, when the strain rate increases, the two bands stay together longer and thus that the onset of localised necking is delayed.

     

Modelling the correlation between the geometrical features and the forming limit strains of perforated Al 8011 sheets using artificial neural network

In the recent years, sheet metals are produced with perforations in various shapes and patterns to improve the appearance of sheet and to save weight of components. As in conventional metal sheets, it is important to form the perforated sheet metals also within their safe strain regions to avoid the forming failures like necking, fracture and wrinkling. The Forming Limit Diagram (FLD) is an appropriate tool to determine the forming limit strains. The limiting strains of perforated sheet metals mainly depend on the geometry of the perforations and forming variables. This leads to large increase in number of test to be conducted with various geometry and forming variables for determining the forming limit strain for perforated sheets. Aiming to reduce the number of experiments needed, in this work, an Artificial Neural Network (ANN) model has been developed for forming limit diagram of perforated Al 8011 sheets based on experimental results and correlated with the geometrical features of the perforated sheets. This model is a feed forward back propagation neural network (BPNN) with a set of geometrical variables as its inputs and the safe true strains as its output. This ANN model can be applied for prediction of FLD of perforated sheet having any geometry.     

Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading

The present paper is concerned with multi-axial ductile fracture experiments on sheet metals. Different stress-states are achieved within a flat specimen by applying different combinations of normal and transverse loads to the specimen boundaries. The specimen geometry is optimized such that fracture initiates remote from the free specimen boundaries. Fracture experiments are carried out on TRIP780 steel for four different loading conditions, varying from pure shear to transverse plane strain tension. Hybrid experimental–numerical analyses are performed to determine the stress and strain fields within the specimen gage section. The results show that strain localization cannot be avoided prior to the onset of fracture. Through-thickness necking prevails under tension-dominated loading while the deformation localizes along a band crossing the entire gage section under shear-dominated loading. Both experimental and simulation results demonstrate that the proposed fracture testing method is very sensitive to imperfections in the specimen machining. The loading paths to fracture are determined in terms of stress triaxiality, Lode angle parameter and equivalent plastic strain. The experimental data indicates that the relationship between the stress triaxiality and the equivalent plastic strain at the onset of ductile fracture is not unique.     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.     

An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.     

孔洞敏感超塑性材料变形的数值分析

本文用两种数值方法,非线性长波分析和刚粘塑性有限元方法研究了孔洞敏感的超塑性材料在单向拉伸和园板涨形中的不均匀变形和断裂过程。分析表明,这种过程是不均匀几何失稳与内部孔洞长大的结合与相互作用的结果。材料的应变速率敏感性指数与孔洞长大速率通过不同的变形机理图控制着这种过程。叠加的静水压力能够改变孔洞敏感材料的断裂模式,从常压下没有宏观颈缩的孔洞断裂到无内部孔洞的外部颈缩断裂。     

Forming and fracture limits of aluminium alloy

Abstract

Forming and fracture limits of an AA 3104-H19 aluminium alloy sheet were studied by hydraulic bulging and Marciniak type deep drawing and tensile tests. The alloy appeared to be highly anisotropic, exhibiting distinctly different fracture patterns in the rolling and transverse directions. The preferred fracture direction was transverse to the rolling direction. In the tensile test, samples loaded in the rolling direction failed transverse to the rolling direction, but in the transverse direction, the fracture was inclined at ～55° to the tensile axis. In some cases, two such competing fractures in the characteristic directions could be observed. Scanning electron microscopy studies revealed a typical ductile fracture pattern. The fracture occurred by shearing in the through thickness direction, and typical alternating shear lips in a direction inclined at ～45° to the through thickness direction could be observed. Forming limit diagrams for both rolling and transverse directions were determined from the experiments. The measured limit strains in uniaxial tension were predicted well by the modified Rice–Tracey theory, but in equibiaxial tension, the theory overestimated the fracture limit strains.     

Stress–strain curves of metallic materials and post‐necking strain hardening characterization: A review

For metallic materials, standard uniaxial tensile tests with round bar specimens or flat specimens only provide accurate equivalent stress–strain curve before diffuse necking. However, for numerical modelling of problems where very large strains occur, such as plastic forming and ductile damage and fracture, understanding the post‐necking strain hardening behaviour is necessary. Also, welding is a highly complex metallurgical process, and therefore, weldments are susceptible to material discontinuities, flaws, and residual stresses. It becomes even more important to characterize the equivalent stress–strain curve in large strains of each material zone in weldments properly for structural integrity assessment. The aim of this paper is to provide a state‐of‐the‐art review on quasi‐static standard tensile test for stress–strain curves measurement of metallic materials. Meanwhile, methods available in literature for characterization of the equivalent stress–strain curve in the post‐necking regime are introduced. Novel methods with axisymmetric notched round bar specimens for accurately capturing the equivalent stress–strain curve of each material zone in weldment are presented as well. Advantages and limitations of these methods are briefly discussed.     

Ductile fracture before localized necking in a strip under tension

Unexpected cracking with a 22° opening angle grew out of a rough-sheared edge before appreciable necking in an 0.79 by 37 mm mild steel strip, which normally fractures after diffuse and then localized oblique necking. From the crack tip, two shear bands formed at 55° to the load direction, consistent with isotropic plane stress characteristics (53° was predicted from anisotropy, but necking in thin strips occurred at 67°). Photomicrographs showed that the 22° crack growth occurred by first tunnelling at mid-thickness, and then spreading along through-thickness shear planes. Springback on unloading caused a 0.038 mm crack closure and local buckling. This form of cracking illustrates a size effect in fracture under macroscopically plane stress. It also gives an example of a local mechanism triggering a fracture mode that can require more total work than an alternative.Analysis of isotropic localized necking shows the equivalent strain at fracture in thin strips to be uniquely related to the Reduction in Squared Thickness (RST). With smooth edges, width and thickness strains before and during necking differed by factors of 1.4 and 1.7; such measures of anisotropy should be routinely found and reported for strips.     

Evaluation of non-linear strain paths using Generalized Forming Limit Concept and a modification of the Time Dependent Evaluation Method

The prediction of formability is one of the most important tasks in sheet metal forming process simulation. The common criterion for ductile fracture in industrial applications is the Forming Limit Diagram (FLD). This is only applicable for linear strain paths. However, in most industrial simulation cases non-linear strain paths occur. To resolve this problem, a phenomenological approach is introduced, the so-called Generalized Forming Limit Concept (GFLC). The GFLC enables prediction of localized necking on arbitrary non-linear strain paths. Another possibility is the use of the Time Dependent Evaluation Method (TDEM) within the simulation as a failure criteria. During the Numisheet Benchmark 1 (2014) a two-stage forming process was performed with three typical sheet materials (AA5182, DP600 and TRIP 780) and three different blank shapes. The task was to determinate the point in time and space of local instability. Therefore the strain path for the point of maximum local thinning is evaluated. To predict the start of local necking the Generalized Forming Limit Concept (GFLC), the Time Dependent Evaluation Method (TDEM) and the modified TDEM were applied. The results of the simulation are compared with the results of the Benchmark experiment.     

Numerical implementation of anisotropic damage mechanics

This paper describes implementation of anisotropic damage mechanics in the material point method. The approach was based on previously proposed, fourth‐rank anisotropic damage tenors. For implementation, it was convenient to recast the stress update using a new damage strain partitioning tensor. This new tensor simplifies numerical implementation (a detailed algorithm is provided) and clarifies the connection between cracking strain and an implied physical crack with crack opening displacements. By using 2 softening laws and 3 damage parameters corresponding to 1 normal and 2 shear cracking strains, damage evolution can be directly connected to mixed tensile and shear fracture mechanics. Several examples illustrate interesting properties of robust anisotropic damage mechanics such as modeling of necking, multiple cracking in coatings, and compression failure. Direct comparisons between explicit crack modeling and damage mechanics in the same material point method code show that damage mechanics can quantitatively reproduce many features of explicit crack modeling. A caveat is that strengths and energies assigned to damage mechanics materials must be changed from measured material properties to apparent properties before damage mechanics can agree with fracture mechanics.     

Failure mode of laser welds in lap‐shear specimens of high strength low alloy (HSLA) steel sheets

In this paper, the failure mode of laser welds in lap‐shear specimens of non‐galvanized SAE J2340 300Y high strength low alloy steel sheets under quasi‐static loading conditions is examined based on experimental observations and finite element analyses. Laser welded lap‐shear specimens with reduced cross sections were made. Optical micrographs of the cross sections of the welds in the specimens before and after tests are examined to understand the microstructure and failure mode of the welds. Micro‐hardness tests were also conducted to provide an assessment of the mechanical properties in the base metal, heat‐affected and fusion zones. The micrographs indicate that the weld failure appears to be initiated from the base metal near the boundary of the base metal and the heat‐affected zone at a distance away from the pre‐existing crack tip, and the specimens fail due to the necking/shear of the lower left load carrying sheets. Finite element analyses based on non‐homogenous multi‐zone material models were conducted to model the ductile necking/shear failure and to obtain the J integral solutions for the pre‐existing cracks. The results of the finite element analyses are used to explain the ductile failure initiation sites and the necking/shear of the lower left load carrying sheets. The J integral solutions obtained from the finite element analyses based on the 3‐zone finite element model indicate that the J integral for the pre‐existing cracks at the failure loads are low compared to the fracture toughness and the specimens should fail in a plastic collapse or necking/shear mode. The effects of the sheet thickness on the failure mode were then investigated for laser welds with a fixed ratio of the weld width to the thickness. For the given non‐homogenous material model, the J integral solutions appear to be scaled by the sheet thickness. With consideration of the plastic collapse failure mode and fracture initiation failure mode, a critical thickness can be obtained for the transition of the plastic collapse or necking/shear failure mode to the fracture initiation failure mode. Finally, the failure load is expressed as a function of the sheet thickness according to the governing equations based on the two failure modes. The results demonstrate that the failure mode of welds of thin sheets depends on the sheet thickness, ductility of the base metal and fracture toughness of the heat‐affected zone. Therefore, failure criteria based on either the plastic collapse failure mode or the fracture initiation failure mode should be used cautiously for welds of thin sheets.     

Role of geometry in plastic instability and fracture of tubes and sheet

Conditions for plastic instability and fracture for biaxially loaded tubes are compared to those for a sheet to assess the role of geometry. Thin-walled tubes of 70-30 brass were loaded in combined axial tension-internal pressure. The strains for diffuse instability, local instability and fracture were measured and compared to results on brass sheet. Uniform deformation (up to diffuse instability) was found to be very sensitive to geometry in agreement with theory. The uniform strain in tubes for axial plane strain is twice that for hoop plane strain and the uniform strain in tubes for balanced biaxial tension is only one third of that for sheet. The strain levels for local instability and fracture did not depend on geometry. No significant differences were found for axial vs. hoop loading in tubes and the critical strain levels for tubes were actually somewhat greater than those for sheet. Although the critical local strains are similar, the amount of useful (genera) deformation beyond diffuse instability for tubes is very limited because localization occurs rapidly. In bulged or punched sheet the geometry is stable and localization occurs gradually, providing significant post-uniform deformation.     

Semi-solid deformation in multi-component nickel aluminide

A systematic study was carried out to determine the solidification and the tensile behaviour of semi-solid multicomponent nickel aluminide. Directionally solidified samples were tested at various temperatures in the mushy (semi-solid) region. A special Gleeble testing procedure was developed where transverse and longitudinal (5 mm) samples were quickly raised to a predetermined temperature in the semi-solid zone and fractured. The fracture stresses were found to decrease monotonically with temperature. The strain to fracture exhibited a ductility minimum at an intermediate temperature in the semi-solid zone. The effect of the solidification process variables, namely, the temperature gradient and velocity, on the fracture stress in the transverse direction was to increase the fracture stress at a given temperature. In the longitudinal direction, the fracture stress decreases with the temperature gradient and was relatively independent of velocity. At the temperature corresponding to the strain minimum, residual microcracks were detected on the fracture surface. The upper hot tearing temperature was noted to be a function of the solidification variables. The amount of strain accommodation and the hot tearing resistance was found to be influenced by the solidification microstructure. Fracture maps which include the transverse fracture stress, temperature, and temperature gradient during solidification (_T-T-G) for the directionally solidified microstructures are presented. A castability map is created from the fracture data.     

Fracture behavior of 9% nickel high-strength steel at various temperatures: Part I. Tensile tests

Fracture behavior of a 9% nickel 1000 MPa grade high-strength steel was investigated with tensile tests at various temperatures. Four critical stresses were found, which determined the fracture behaviors at various temperatures. Various fracture behaviors could be classified into three categories: (1) at −196 °C, a longitudinal crack initiated from the center of the necking region and propagated along the tensile direction to the regions close to both ends of the necking, it then changed the orientation and developed into two transverse cracks which propagated into opposite directions on two separated cross-sections. (2) In the range of −30 °C to 20 °C, the fracture surfaces were composed of typical center-fibrous-initiation region, middle shear-radical region and outer shear-lip region. (3) In the range of −150 °C to −60 °C, the middle shear-radiation region showed a very rough pattern with several convex ridges. Fracture mechanisms were analyzed by combining various fracture morphologies with FEM-calculated results of stress and strain.     

Study of large plastic strains and fracture in metal elements by photoelastic coating method

The photoelastic coating method has been developed to investigate large strains in metals with the help of the coatings made from sensitive optical materials. The strain changes have been within the range from ?50% to 220%. Some fracture mechanics problems considering large strains were solved: first, the stress-strain condition was determined at the localized necking of a thin steel bar; second, the stress field near the sharp notch's tip in an aluminum bar was obtained; also, the kinetics of plastic strain development was studied. Plane problems of strain determination at the macrolevel were investigated. The investigations were sponsored by the Russian Fund of Fundamental Investigations (Project No. 02-01-00222).