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plane-stress deformation

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Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006282
EISBN: 978-1-62708-169-6
... forces holding the atoms of a given plane in position are stronger than the forces holding two planes together. Thus, when a crystal is subjected to a stress greater than the elastic limit, the bonds holding the planes together are the first to yield, and deformation occurs by slipping between two...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004030
EISBN: 978-1-62708-185-6
... ¯ ) ε ¯   = 2 ( 2 + R ) 3 ( 1 + R ) ε 1 Plane-strain compression of sheet assuming uniform deformation and planar isotropy (R 0 ° = R 90 ° =R 45 ° =R)  Through-thickness true stress σ 3  Through-thickness true strain ε 3  Effective stress...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004018
EISBN: 978-1-62708-185-6
... that of a pure, ideal crystal ( Fig. 1a ). In the case of the ideal crystal, shear displacement would occur by simultaneous relative motion of all the atoms along a slip plane ( Fig. 1b ). In this idealized case, calculated stresses on the order of 10 to 30 GPa (1 to 5 × 10 3 ksi) would be required...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006774
EISBN: 978-1-62708-295-2
... degree of constraint associated with the presence of a cracklike imperfection. Under plane-stress conditions, a fracture is typically considered brittle at the macroscale if it is oriented orthogonally to the maximum normal stress (condition 4 in Fig. 14 ). A fracture is typically considered to be...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004028
EISBN: 978-1-62708-185-6
... planes, and since a threshold shear stress is required to activate dislocations, it turns out that the orientation of the crystals will affect the stress required to deform the aggregate. As a consequence, there is a direct connection between texture and anisotropic mechanical response. Anisotropy means...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005456
EISBN: 978-1-62708-196-2
... the unknown constant determined by the stress compatibility at the interface of these zones. This approach has been extended to other steady-state metalforming problems, such as rod drawing, tube drawing, plane-strain rolling (bloom, slab, or strip), and plane-strain strip deep drawing (sheet forming...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005461
EISBN: 978-1-62708-196-2
... fracture during the double-extrusion forging of aluminum alloy 6061. Grid deformations on the middle longitudinal plane are shown. The stress-strain states are defined by the insert, σ 3 is perpendicular to the plane of the schematic bulging the free surface. Fig. 32 Progression of surface...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003024
EISBN: 978-1-62708-200-6
... of crazing in polymers are discussed below. When a tensile stress is applied to some polymers, the first stage of plastic deformation is the formation of voids in a plane perpendicular to the direction of the applied load. In contrast to metals, these voids do not coalesce into a crack, but instead...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005458
EISBN: 978-1-62708-196-2
... theories of cavitation in metallic materials, several key ideas were developed for creep deformation and then applied to superplastic and conventional hot deformation. In these approaches, creep at low stresses and the diffusional contribution to cavity enlargement were considered the most important issues...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006797
EISBN: 978-1-62708-295-2
... temperature. In sections that do contain stress raisers, net section yielding can still occur if the state of stress is plane stress; that is, one normal stress component is 0. If the stress raiser results in sufficient constraint to produce plane strain, then gross yielding and distortion will not be...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005417
EISBN: 978-1-62708-196-2
... alternative to this localized determination of friction conditions is to obtain an average frictional shear stress and/or an average coefficient of friction over the whole interface. Methods in this group include plane-strain drawing ( Ref 27 ) and plane-strain compression ( Ref 28 ). A twist compression...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009007
EISBN: 978-1-62708-185-6
... 9 shows a plate deformed in three-point bending. The principal stress and strains developed during bending are defined in Fig. 10 . The critical parameter is width-to-thickness ratio, w / t . if w / t < 8, bending occurs under plane-strain conditions (ε 2 = 0), and σ 2 /σ 1 = 0.5. If w...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004017
EISBN: 978-1-62708-185-6
... deformation finite-element modeling forgeability test fracture indentation test plane-strain compression test ring compression test strain strain rate stress tension test workability workability analysis workability tests WORKABILITY refers to the relative ease with which a metal can be...
Book Chapter

By Sammy Tin
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005404
EISBN: 978-1-62708-196-2
... velocity, v c , can be expressed as ( Ref 11 ): (Eq 25) v c = D ν σ n b 2 k T where D v is the vacancy diffusion coefficient, and σ n is the stress component normal to the slip plane. The creep strain rate can then be expressed as...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004029
EISBN: 978-1-62708-185-6
... aligned with the maximum shear stress poles that correspond to the deformation mode. This rule implies that, in a rolling experiment, only those ⟨110⟩ axes are preferred that are near the normals to planes that are inclined at 45° to the rolling plane ( Fig. 25 ). According to such a rule, only the...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006252
EISBN: 978-1-62708-169-6
... stress develops in the surface upon immersion. The out-of-plane component is constrained to zero in the surface, but the in-plane tensile stresses build up in the surface. These rapidly reverse as the interior yields, and a large biaxial compressive stress develops in the colder strong surface, in...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009003
EISBN: 978-1-62708-185-6
... shear stress, τ, is given by: (Eq 2b) τ = P  shear  A a b = P A cos λ cos θ When the plane and direction for which the shear stress is determined is a crystallographic slip system, and the shear stress is that which activates plastic deformation, then Eq 2(b) is...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004020
EISBN: 978-1-62708-185-6
... may be resisted at grain-boundary steps, ledges, and particles (not shown). Stress concentration leads to initation of glide along slip planes in the favored orientations. Thus, discontinuities such as ledges, nondeformable particles, and dispersoids on the grain boundaries act as dislocation sources...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004019
EISBN: 978-1-62708-185-6
... short dislocation loops. Thin-foil TEM specimen prepared parallel to the rolling plane. Original magnification 62,000× For polycrystalline specimens deformed to large strains, such as heavily cold-rolled sheet or strip, the dislocation density is very high, and the microstructure becomes extremely...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... the limited number of modes of deformation due to crystallographic slip or twinning. The most common slip systems for hcp titanium consist of basal < a > (slip on the basal plane along an < a > direction), prism < a > (slip on a prism plane along an < a > direction), and...