Comments on anisotropic yield criteria

Limitations of several anisotropic yield criteria are discussed. Hill's 1948 criterion overestimates the variation of yield strength with direction, while the specializations of Hill's 1979 theory assume planar isotropy. Shear stress terms cannot simply be included in either the author's 1979 criterion or in Hill's 1979 general criteria.It is suggested that the author's criterion be modified so that it is expressed in terms of principal stresses rather than referring stresses to the symmetry axes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25901/1/0000464.pd

The influence of strain-path changes on forming limit diagrams of A1 6111 T4

The effects of changing strain-paths on forming limits of aluminum alloy 6111 T4 have been investigated by determining forming limit diagrams (FLDs) of specimens prestrained to several levels in uniaxial, plane strain and biaxial tension, parallel and perpendicular to the prior rolling direction. Prestraining in biaxial tension generally lowers the entire FLD, whereas prestraining in uniaxial tension raises the limits on the right hand side of the FLD without much effect on the left hand side, when the direction of the largest principal strain does not change. If the directions of the principal strains are rotated, prestraining in uniaxial or plane strain tension lowers the forming limits for most of the FLD range.A general finding was that, after prestraining, the amount of the additional plane strain deformation possible before failure depends on the effective strain during prestrain, regardless of the original strain-path. Finally, an example of the importance of strain-path changes in a stamping of an aluminum automobile part is presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31309/1/0000217.pd

Yield loci of anisotropic sheet metals

Four sheet metals, having quite different combinations of R-values and strain-hardening behavior were tested in uniaxial tension, uniaxial (through thickness) compression, balanced biaxial tension (bulge test), and plane-strain compression. The results were compared with predictions based upon three different anisotropic yield criteria. Although no single yield criterion proved to describe adequately all of the test results, different criteria provided the best agreement with particular metals. Results from through-thickness compression and bulge tests were nearly identical.In bulge testing, strains were determined from photographs of printed grids while the radius of curvature at the top of the dome was obtained using a projected fringe technique that involved a holographic grating. Radii measured by this technique were smaller for all materials than those measured by the conventional spherometer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25446/1/0000896.pd

Using coupled micropillar compression and micro-Laue diffraction to investigate deformation mechanisms in a complex metallic alloy Al13Co4

In this investigation, we have used in-situ micro-Laue diffraction combined with micropillar compression of focused ion beam milled Al13Co4 complex metallic alloy to study the evolution of deformation in Al13Co4. Streaking of the Laue spots showed that the onset of plastic flow occured at stresses as low as 0.8 GPa, although macroscopic yield only becomes apparent at 2 GPa. The measured misorientations, obtained from peak splitting, enabled the geometrically necessary dislocation density to be estimated as 1.1 x 1013 m-2

Convexity restrictions on non-quadratic anisotropic yield criteria

Examination of Hill's 1979 anisotropic yield criterion [Math. Proc. Camb. Phil. Soc. 85, 179 (1979)] shows that for Cases I, II and III, there are combinations of m and R for which the yield loci are outwardly concave or even unbounded. For Case I, all loci are concave unless m = 2. For Cases II and III, the combinations of m and R which lead to concavity and unboundedness have been established. Case IV and Hosford's criterion have no problem regions as long as m [ges] 1.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26986/1/0000553.pd

Texture development in polyethylene II. Unidirectional rolling

The effect of degree of strain on texture development in high-density polyethylene has been studied by pole figure analysis for unidirectional rolling. The crystallite orientation distribution in rolling textures has been quantified with an efficient technique which fits three-parameter, two-dimensional Gaussian-type distributions to pole figure intensity data around ideal single crystal orientations. During flat rolling of polyethylene a texture consisting of a strong (100) [001] component and a weak (110) [001] component develops continuously from the lowest true strain of 0.24 (21% reduction) up to the highest true strain of 1.36 (74% reduction). The peak intensity of the Gaussian distributions of both (100) [001] and (110) [001] components increase continuously to the highest strain. The maximum angular breadth of both component distributions, which are roughly perpendicular to the strain direction, remains constant with increasing strain. The minimum angular breadth of both component distributions, which are roughly parallel to the strain direction, decreases continuously owing to gradual alignment of the covalently bonded chain backbone parallel to the strain direction. The development of the (100) [001] component is explained by slip on (100) planes while the weak (110) [001] component is explained by slip on (110) planes. Although the latter component was previously attributed to (110) or (310) relaxation twinning, this seems unlikely because of the lateral constraint during plane strain deformation conditions used in this study.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38858/1/090270907_ftp.pd

Texture development in polyethylene. I. Uniaxial extension and uniaxial compression

Texture development of high-density polyethylene has been studied by x-ray diffraction at various strains for uniaxial extension, as achieved by uniaxial tension and extrusion, and for uniaxial compression. Pole distributions were measured for the (100), (200), (020), and (011) reflections. Textures were described by ideal single-crystal orientations with inverse pole figures. In uniaxial extension, samples were deformed up to true strains of 1.83 (reductions of up to 84%). After a strain of 0.55, the c axis oriented at 35° from the extension axis and with increasing strain approached the extension axis. This was attributed to initial (110) or (310) twinning in combination with (100) slip, followed subsequently by [001] slip. In compression, samples were deformed up to true strains of 1.83 (reductions up to 84%). The texture consisted of strong components of the compression axis near (100) and weaker components near (110). At higher strains the intensity of the near-(100) components decreased, whereas the near-(110) components became more intense. The near-(100) components are explained by slip on (100) planes. The growth of the near-(110) components at the expense of the near-(100) components can be explained by relaxation twinning of the near-(100) components.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38857/1/090270906_ftp.pd

The plastic deformation of magnesium : technical report

http://deepblue.lib.umich.edu/bitstream/2027.42/5928/5/bac5841.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/5928/4/bac5841.0001.001.tx