Farhang Pourboghrat

Plane stress yield function for aluminum alloy sheets—part 1: theory

Abstract A new plane stress yield function that well describes the anisotropic behavior of sheet metals, in particular, aluminum alloy sheets, was proposed. The anisotropy of the function was introduced in the formulation using two linear transformations on the Cauchy stress tensor. It was shown that the accuracy of this new function was similar to that of other recently proposed non-quadratic yield functions. Moreover, it was proved that the function is convex in stress space. A new experiment was proposed to obtain one of the anisotropy coefficients. This new formulation is expected to be particularly suitable for finite element (FE) modeling simulations of sheet forming processes for aluminum alloy sheets.

Non-orthogonal constitutive equation for woven fabric reinforced thermoplastic composites

One of the ultimate objectives of this study was to investigate the feasibility of shaping preconsolidated woven FRT (fabric reinforced thermoplastics) using stamp thermo-hydroforming, a new forming method for composite manufacturing. A new constitutive model has been developed based on a homogenization method by considering the microstructures of composites including both the mechanical and structural properties of fabric reinforcement. In particular, the current model aims to account for the effect of the fiber strength difference and orientation on anisotropy and also to simulate shear deformation without significant length change, common in FRT composite forming. For validation purposes, the model was implemented in an explicit dynamic finite element code and tested for in-plane simple shear, pure shear, uniaxial tension, and draping behavior of woven composites.

Earing predictions based on asymmetric nonquadratic yield function

A nonquadratic yield function (Yld96; Barlat, F., Maeda, Y., Chung, K., Yanagawa, M., Brem, J.C., Hayashida, Y., Lege, D.J. Matsui, K., Murtha, S.J., Hattori, S., Becker, R.C., Makosey, S., 1997. Yield function development for aluminium alloy sheet. J. Mech. Phys. Solids, 45, 1727) which simultaneously accounts for the anisotropy of uniaxial yield stresses and r values was newly implemented in a finite element code. Yield surface shapes, yield stress and r-value directionalities of Yld96 were investigated and compared with those of the previous yield function, Yld91 (Barlat, F., Lege, D.J., Brem, J.C. 1991a. A six-component yield function for anistropic metals. Int. J. Plasticity, 7, 693). Complete formulations for Yld96 implementation and the calculation of coefficients were also discussed for the convenient use of Yld96. A 2090-T3 aluminum alloy sheet sample was modeled and earing formation during a cup drawing test was simulated using the FEM code. The results of earing and thickness strain profiles were compared with the results obtained with Yld91. Investigations were further carried out with a translated yield surface to account for the strength differential effect observed in this material. Computation results with the translated yield surface were in very good agreement with experimental results. It was shown that the yield surface shape and translation have a significant influence on the prediction of the cup height profile during the drawing of a circular blank.

Springback in plane strain stretch/draw sheet forming

Abstract Accurate prediction of springback is essential for the design of tools used in automotive sheet stamping operations. The plane strain stretch/draw operation presents a complex form of springback occurring in sheet metal forming since the sheet undergoes stretching, bending and unbending deformations. The two-dimensional draw bending is an example of such an operation in which the complex stress-strain states in the sheet cause the formation of side wall curls after the sheet is allowed to unload. Accurate prediction of the side wall curl requires using finite element shell models which can account for curvature and through-thickness stresses caused by bending and unbending of the sheet. Since such models are generally slow and expensive to use, an alternative and efficient method of predicting side wall curls will be desirable. This paper describes a novel and robust method for predicting springback in general and side wall curls in the two-dimensional draw bending operation as a special case, using moment-curvature relationships derived for sheets undergoing plane strain stretching, bending and unbending deformations. This model modifies a membrane finite element solution to calculate through-thickness strains and stresses and springback. Accuracy of this models predictions are verified by comparisons with finite element (ABAQUS) and experimental results.

Prediction of spring-back and side-wall curl in 2-D draw bending

Accurate prediction of spring-back is essential for the design of tools used in automotive sheet-stamping operations. The 2-D draw bending operation presents a complex form of spring-back occurring in sheet-metal forming since the sheet undergoes stretching, bending and unbending deformations. These three sets of deformation can create complex stress-strain states in the sheet which result in the formation of side-wall curls after the sheet is allowed to unload. Accurate prediction of the side-wall curl requires using finite-element shell models which can account for curvature and stress variation through the thickness caused by bending and unbending of sheet. Since such models are generally computationally intense, an alternative and efficient method of predicting side-wall curls is desirable. This paper describes a novel and robust method for predicting spring-back and side-wall curls in 2-D draw bending operations, using moment-curvature relationships derived for sheets undergoing plane-strain stretching, bending and unbending deformations. This model makes use of the membrane finite-element solution to calculate spring-back. The accuracy of the model is verified by comparison with finite element (ABAQUS) and experimental results.

Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method

To reduce the computational time of finite element analyses for sheet forming, a 3D hybrid membrane/shell method has been developed and applied to study the springback of anisotropic sheet metals. In the hybrid method, the bending strains and stresses were calculated as post-processing, considering the incremental change of the sheet geometry obtained from the membrane finite element analysis beforehand. To calculate the springback, a shell finite element model was used to unload the sheet. For verification purposes, the hybrid method was applied for a 2036-T4 aluminum alloy square blank formed into a cylindrical cup, in which stretching is dominant. Also, as a bending-dominant problem, unconstraint cylindrical bending of a 6111-T4 aluminum alloy sheet was considered. The predicted springback showed good agreement with experiments for both cases.

Sheet hydroforming of woven FRT composites: non-orthogonal constitutive equation considering shear stiffness and undulation of woven structure

For the simulation of sheet hydroforming for the shaping of woven fabric reinforced thermo-plastic (FRT) composites, a non-orthogonal constitutive model was developed based on a homogenization method by considering the microstructures of composites including mechanical and structural properties of the fabric reinforcement. This model is modified to capture the wrinkling behavior due to the undulation geometry of the woven structure and shear stiffness at the crossover of the warp and weft yarns of woven FRT composites. The model was implemented in an explicit dynamic finite element code to analyze the forming behavior of woven FRT during the stamp thermo-hydroforming process. Wrinkling behavior was investigated based on the application of a counteracting fluid pressure and changes to the initial blank shape.

Finite element analysis of textile composite preform stamping

The forming or draping of a textile composite preform may result in large changes in the fibrous microstructure of the preform. This change in the local fiber orientation leads to significant changes in the fabric permeability as well as the mechanical properties of the ensuing composite structure. Therefore, this change in orientation of the tows of the preform needs to be known accurately to calculate the various effective properties of the composite. A new finite element approach for stamping analysis of a plain-weave textile composite preform has been developed. This model is simple, efficient and can be used in the existing finite element codes. The model represents the preform as a mesh of 3-D truss elements and 3-D shell elements. The truss elements model the tows, which are allowed to both scissor and slide relative to one another. The shell elements represent a fictitious material that accounts for inter-tow friction and fiber angle jamming. The model takes into account large strains and large deformations. In-plane uniaxial tension tests have been performed on plain-weave specimens for determining the constitutive law of the transforming medium and to show the inter-tow sliding. Application of the model is demonstrated by simulating the stamping of a preform by a spherical punch. The results from the simulation show good correlation with results from the experiments.

Influence of initial back stress on the earing prediction of drawn cups for planar anisotropic aluminum sheets

Abstract Anisotropy is closely related to the formability of sheet metal and should be considered carefully for more realistic analysis of actual sheet metal forming operations. In order to better describe anisotropic plastic properties of aluminum alloy sheets, a planar anisotropic yield function which accounts for the anisotropy of uniaxial yield stresses and strain rate ratios simultaneously was proposed recently. This yield function was used in the finite element simulations of cup drawing tests for an aluminum alloy 2008-T4. Isotropic hardening with a fixed initial back stress based on experimental tensile and compressive test results was assumed in the simulation. The computation results were in very good agreement with the experimental results. It was shown that the initial back stress as well as the yield surface shape have a large influence on the prediction of the cup height profile.

The Effect of Cooling Rate on Grain Orientation and Misorientation Microstructure of SAC105 Solder Joints Before and After Impact Drop Tests

The effect of different cooling rates on as-assembled Sn1.0Ag0.5Cu (wt.%) solder joints was investigated by using orientation imaging microscopy to characterize evolution of the microstructure and orientation distribution on test samples before and after shock testing. Evolution of the microstructure of joints located near the corners after shock testing differed substantially for samples cooled at different rates after fabrication. After shock and impact testing, much recrystallization was observed for the rapidly cooled samples; this led to polycrystalline microstructures that were effective in absorbing impact energy, by incorporating a growing crack into the recrystallized tin microstructure rather than the lower-energy intermetallic interface, and thus prolonging life. The slowly cooled samples contained large amounts of (301)[