R.H. Wagoner

Dislocation and grain boundary interactions in metals

Abstract The passage of dislocations through grain boundaries in face centered cubic and body centered cubic polycrystalline metals was studied using dynamic in situ high voltage electron microscopy (HVEM), static transmission electron microscopy (TEM), and anisotropic elastic stress analysis. Several conclusions were reached: (1) when dislocations propagate across grain boundaries, the activated slip system can be predicted from pile-up properties and grain boundary orientation using a combined criterion based on boundary geometric factors and internal stresses; (2) different grain boundaries impede dislocation slip propagation to different degrees, the calculated value of the pile-up obstacle stress varying from 280 to 870 MPa for dislocation transmission through a grain boundary in 304 stainless steel; (3) dynamic in situ straining of miniature tensile specimens reveals additional modes of dislocation and grain boundary interactions that were hidden from static TEM observations. In connection with the last conclusion, simultaneous dislocation transmission and reflection was activated by a stressed pile-up and a complex mechanism involving coordinated movements of four sets of dilocations in and near a grain boundary was observed.

Simulation of springback

Springback, the elastically-driven change of shape of a part after forming, has been simulated with 2-D and 3-D finite element modeling. Simulations using solid and shell elements have been compared with draw-bend measurements presented in a companion paper. Plane-stress and plane-strain simulations revealed the dramatic role of numerical tolerances and procedures on the results. For example, up to 51 integration points through the sheet thickness were required for accuracy within 1%, compared with 5–9 typically acceptable for forming simulations. Improvements were also needed in the number of elements in contact with the tools, and in the numerical tolerance for satisfying equilibrium at each step. Significant plastic straining took place in some cases upon unloading; however the choice of elastic–plastic unloading scheme had little effect on the results. While 2-D simulations showed good agreement with experiments under some test conditions, springback discrepancies of hundreds of percent were noted for one alloy with sheet tension near the yield stress. 3-D simulations provided much better agreement, the major source of error being identified as the presence of persistent anticlastic curvature. Most of the remaining deviation in results can be attributed to inaccuracies of the material model. In particular, the presence of a Bauschinger effect changes the results markedly, and taking it into account provided good agreement. Shell elements were adequate to predict springback accurately for R/t greater than 5 or 6, while solid elements were required for higher curvatures. As R/t approaches 2, springback simulated with solid elements tends to disappear, in agreement with measurements presented in the companion paper and in the literature.

Role of plastic anisotropy and its evolution on springback

Springback angles and anticlastic curvatures reported for a series of draw-bend tests have been analyzed in detail using a new anisotropic hardening model, four common sheet metal yield functions, and finite element procedures developed for this problem. A common lot of 6022-T4 aluminum alloy was used for all testing in order to reduce material variation. The new anisotropic hardening model extends existing mixed kinematic/isotropic and nonlinear kinematic formulations. It replicates three principal characteristics observed in uniaxial tension/compression test reversals: a transient region with low yield stress and high strain hardening, and a permanent offset of the flow stress at large subsequent strains. This hardening model was implemented in ABAQUS in conjunction with four yield functions: von Mises, Hill quadratic, Barlat three-parameter, and Barlat 1996. The simulated springback angle depended intimately on both hardening law after the strain reversal and on the plastic anisotropy. The springback angle at low back forces was controlled by the hardening law, while at higher back forces the anticlastic curvature, which depends principally on yield surface shape, controlled the springback angle. Simulations utilizing Barlats 1996 yield function showed remarkable agreement with all measurements, in contrast to simulations with the other three yield functions.

Measurement of springback

Abstract Springback, the elastically-driven change of shape of a part after forming, has been measured under carefully-controlled laboratory conditions corresponding to those found in press-forming operations. Constitutive equations emphasizing low-strain behavior were generated for three automotive body alloys: drawing-quality silicon-killed steel; high-strength low-alloy steel; and 6022-T4 aluminum. Strip draw-bend tests were then conducted using a range of die radii (3

Metal Forming Analysis

1. Mathematical background 2. Introduction to the finite element method 3. Finite elements for large deformation 4. Typical finite elements 5. Classification of finite element formulations 6. Auxiliary equations: contact, friction, incompressibility 7. Thermo-mechanical principles 8. Sheet metal formability tests 9. Steady state forming problems 10. Forging analysis 11. Sheet forming analysis 12. Recent research topics.

Forming of tailor-welded blanks

Beginning in 1992, tailor-welded blanks (TWBs) were used in the United States automotive industry to consolidate parts, reduce tolerances, save weight, and increase stiffness. This business is expanding rapidly; more than

A rigid-viscoplastic finite element program for sheet metal forming analysis

500 million of annual TWB sales are expected by 1997. Welds in steel are generally stronger than the base material, such that weld failure by preferential localization is not a critical issue. However, the forming characteristics of TWBs must be understood in order to design and produce high-quality parts with reasonable production and tooling costs. Three formability issues were addressed in this study: the intrinsic ductility and relative formability of three weld types (CO2 and Nd:YAG laser welds and mash-seam welds with and without mechanical postweld processing); the value and correspondence of mechanical tests to each other and to press performance; and the prediction of the forming behavior using the finite element method (FEM). Two failure modes for TWBs were identified. While the local ductility of welds can differ greatly, little difference in press formability was measured among the weld types. More important than weld ductility are the changed deformation patterns which depend on the differential strength but depend little on local weld prop-erties. Finite element method (FEM) simulations of dome tests and scale fender-forming operations show good agreement with measurements, as long as boundary conditions are known accurately. The importance of weld-line displacement is discussed and several simulations are compared with ex-periments.

Plastic behavior of aluminum-killed steel following plane-strain deformation

Abstract A finite element modeling (FEM) program has been formulated to simulate a general three-dimensional sheet stretching operation. The program is based on an anisotropic, rigid-viscoplastic material model and utilizes triangular, plane stress elements incorporating a membrane approximation. These features are aimed at reducing CPU time for realistic industrial applications while retaining the necessary complexity of material behavior. An incremental theory of plasticity based on Hills new theory of anisotropy and on a minimum plastic work path over the time step is employed. Special algorithms for dealing with die contact condition, material unloading and Coulomb friction have been developed. Simulations of stretch forming using two punch-and-die configurations are presented, and one of the results is compared with results appearing in the literature. Simulations of these operations using finer meshes and smaller time steps demonstrate the robustness of the formulation. Although the program is unoptimized, initial CPU times suggest that the program is suitable for large-scale industrial forming simulations.

Anisotropic hardening equations derived from reverse-bend testing

Aluminum-killed steel sheets have been subjected to plane-strain prestrain in three ways: two-pass rolling, multi-pass rolling, and inplane, plane-strain tension. Subsequent uniaxial tensile tests were performed to evaluate the residual work-hardening behavior. The subsequent hardening curves depended primarily on the relative direction between major strain axes in the two deformation stages and very little on the specific prestrain procedure. These curves showed high initial yield stresses followed by a region of low (or negative) work hardening rate. This behavior contrasted with earlier results for 70/30 brass sheet, and a model of subsequent tensile behavior based on a strain-induced stress transient emerged.

Modeling of the friction caused by lubrication and surface roughness in sheet metal forming

Abstract The plastic response of materials during reverse loading has practical consequences for common sheet forming operations in terms of loads, localization behavior, and springback. However, it is difficult to measure the reverse loading (Bauschinger effect) in sheet materials because of their propensity to buckle. A simple reverse-bend test was constructed and used to investigate the cyclic loading of three automotive body alloys. The results showed that consideration of the Bauschinger effect is essential to obtaining agreement with such results. An inverse procedure was used to determine anisotropic hardening law parameters. Laws obtained in this way were compared with ones generated by more sensitive tension-compression tests appearing in the literature for the same alloys. The two laws were significantly different, but both produced accurate simulations of reverse-bend test load–displacement curves. Several artificial material models were then constructed to simulate the reverse-bend test and thus to probe its sensitivity to material constitutive equation details. For materials whose reverse-loading response varies with the level of prestrain, as is the case for each of the three alloys tested, a wide range of constitutive response is capable of producing identical reverse-bending behavior. The results show that inverse procedures applied to the reverse-bend test do not provide unique results, and thus the usefulness of the reverse-bend test for such investigations is limited.