An Analytical Model for Estimating the Bending Curvatures of Metal Sheets in Laser Peen Forming.

Laser peen forming (LPF) is suitable for shaping sheet metals without the requirement for die/mold and without causing high temperatures. An analytical model for estimating the bending curvatures of LPF is convenient and necessary for better understanding of the physical processes involved. In this paper, we describe a new analytical model based on internal force balance and the energy transformation in LPF. Experiments on 2024 aluminum alloy sheets of 1-3 mm thickness were performed to validate the analytical model. The results showed that for 1 mm and 3 mm thick-thin plates, the curvature obtained by the analytical model changes from -14 × 10-4 mm-1 and -1 × 10-4 mm-1 to 55 × 10-4 mm-1 and -21 × 10-4 mm-1, respectively, with the increase of laser energy, which is consistent with the experimental trend. So, when either the stress gradient mechanism (SGM) or the shock bending mechanism (SBM) overwhelmingly dominated the forming process, the analytical model could give relatively accurate predicted curvatures compared with the experimental data. Under those conditions where SGM and SBM were comparable, the accuracy of the model was low, because of the complex stress distributions within the material, and the complex energy coupling process under these conditions.

Differential regulation of tumor angiogenesis by distinct ErbB homo- and heterodimers.

Interactions between cancer cells and their microenvironment are critical for the development and progression of solid tumors. This study is the first to examine the role of all members of the ErbB tyrosine kinase receptors (epidermal growth factor receptor [EGFR], ErbB-2, ErbB-3, or ErbB-4), expressed singly or as paired receptor combinations, in the regulation of angiogenesis both in vitro and in vivo. Comparison of all receptor combinations reveals that EGFR/ErbB-2 and ErbB-2/ErbB-3 heterodimers are the most potent inducers of vascular endothelial growth factor (VEGF) mRNA expression compared with EGFR/ErbB-3, EGFR/ErbB-4, ErbB-2/ErbB-4, and ErbB-3/ErbB-4. Immunohistochemistry of tumor xenografts overexpressing these heterodimers shows increased VEGF expression and remarkably enhanced vascularity. Enhanced VEGF expression is associated with increased VEGF transcription. Deletional analysis reveals that ErbB-mediated transcriptional up-regulation of VEGF involves a hypoxia-inducible factor 1-independent responsive region located between nucleotides -88 to -66 of the VEGF promoter. Mutational analysis reveals that the Sp-1 and AP-2 transcription factor binding elements within this region are required for up-regulation of VEGF by heregulin beta1 and that this up-regulation is dependent on the activity of extracellular signal-related protein kinases. These results emphasize the biological implications of cell signaling diversity among members of the ErbB receptor family in regulation of the tumor microenvironment.