Forging limits for an aluminum matrix composite: Part II. Analysis
- PDF / 1,066,946 Bytes
- 10 Pages / 598 x 778 pts Page_size
- 64 Downloads / 225 Views
I.
INTRODUCTION-
THE experimental forging limits of 2014 A1/15 vol pct A1203 have been determined as a function of strain state in a companion article, tu To develop a fundamental understanding of the magnitudes of the strains associated with incipient cracking, it is necessary to calculate the forging limits analytically for comparison with the experimental results. A reasonable approach for the analysis is based on the assumption that materials contain defects, t2j These defects can accelerate local deformation in the defect region, while a macroscopically homogeneous state of stress is applied to the overall sample. This can cause the growth of a defect until material separation or failure occurs in the defect region. In the composite material of interest, the defects may arise from the presence of nondeformable A1203 particles, a nonuniform distribution of the A1203 particles and matrix grain sizes, cracked A1203 particles and porosity, etc. For simplicity, the sample was assumed to be subjected to a macroscopically linear strain path (i.e., a constant ratio of compressive to tensile strain). However, microscopically, the strain path can change due to the concentrated stresses and/or strains induced by the local defects. Prediction of local-limit strain 13-8] in composites by finite element modeling of strain concentration at many particles, and the coalescence of voids, is prohibitively D.-G.C. SYU, formerly Graduate Student, the University of Michigan, is Senior Engineer, Taipei Municipal Government, Hsintien, Taipai, Taiwan, Republic of China. A.K. GHOSH, Professor of Materials Science and Engineering, is with the University of Michigan, Ann Arbor, MI 48109-2136. Manuscript submitted August 11, 1992. METALLURGICAL AND MATERIALS TRANSACTIONS A
time consuming and costly. In these calculations, the resuits often become less accurate due to many numerical approximations. Thus, a simple method was adopted following the work of Marciniak and Kuczynski (MK) t21 which represents the defects by an equivalent geometric inhomogeneity (i.e., variation in cross-sectional area). In their analysis, a groove running in a direction perpendicular to the larger principal stress (~1) was considered in a sheet metal subjected to biaxial tension when the ratio of the principal stresses was 0.5 < o'2/cr~ -< 1, as shown in Figure 1. In Figure 1, the local effective strain in the groove (region B) begins to concentrate gradually under biaxial tension and eventually reaches the fracture or infinite strain ratio (ratio of incremental compressive strain, de~, to incremental tensile strain, de2). The limiting strain state in their analysis is, then, defined as the strain state in region A when the local effective strain in region B reaches the failure criterion. They reported that the initial inhomogeneity of the material, f = tB/tA, exerts a great influence on the limiting strain. They also concluded that the inhomogeneity of the sheet metal results from other defects, such as a nonuniform distribution of impurities, varying texture
Data Loading...
