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plane-stress elastic model

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Published: 01 January 1986
Fig. 2 Plane-stress elastic model. More
Image
Published: 15 December 2019
Fig. 2 Plane-stress elastic model More
Series: ASM Handbook Archive
Volume: 10
Publisher: ASM International
Published: 01 January 1986
DOI: 10.31399/asm.hb.v10.a0001761
EISBN: 978-1-62708-178-8
.... The article also outlines the applications of x-ray diffraction residual stress measurement with examples. materials characterization plane stress elastic model residual stress analysis single-angle diffraction two-angle diffraction X-ray diffraction Overview Introduction In x-ray...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003387
EISBN: 978-1-62708-195-5
..., and curling of axially loaded curved flanges. Analytical models for calculating out-of-plane stresses due to direct and indirect loads have been developed for most cases of practical interest to structural engineers. The approaches used in these models have included simple mechanics of materials...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005424
EISBN: 978-1-62708-196-2
...-packed planes in close-packed directions. Both relations exhibit the anisotropy present at the crystal level and together provide a physically-motivated description of a crystalline material behavior. The anisotropic behavior at the crystal level implies that stress and deformation is not uniform over...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005412
EISBN: 978-1-62708-196-2
... of the interface plane. Model-Informed Atomistic Modeling of Interface Structures The concept of model-informed atomistic modeling of interfaces is based on the analysis by Ashby ( Ref 12 ) of the role of modeling and empiricism in reaching engineering solutions. A purely empirically based approach, as well...
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006307
EISBN: 978-1-62708-179-5
.... The preferred slip plane is the one with the densest atomic packing, and the preferred direction is the direction that has the highest linear density. There are two types of dislocations: edge and screw. For a screw dislocation, the direction of motion is perpendicular to the stress direction, but for an edge...
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006632
EISBN: 978-1-62708-213-6
... of industrial metallurgical, process development, and failure analysis investigations undertaken at Lambda Research. X-ray diffraction residual-stress techniques stress measurement plane-stress elastic model Overview Introduction Residual stresses generally are caused by nonuniform thermal...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003399
EISBN: 978-1-62708-195-5
... employed on a unit cell representation of the structure, as illustrated in Fig. 2 . Generalized plane strain is often used in the FEM calculations, and either a constant stress or a constant displacement boundary condition is specified on plane BC . The boundary condition on face AB is not well...
Book Chapter

Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003377
EISBN: 978-1-62708-195-5
... are usually randomly placed, there is no preferred direction in the transverse x 2 x 3 plane, which implies that the UDC is statistically transversely isotropic. Experimental determination of the properties of homogeneous materials is based on induction of homogeneous states of stress and strain...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003262
EISBN: 978-1-62708-176-4
... deformation prevails. Because of this, the elastic modulus in plane-strain (Eq 35) E ′ = E 1 − ν 2 is employed, and the plastic flow stresses ( Eq 34 ) are multiplied by (2 / 3 ). These approximate plane-strain adjustments are considered adequate when the simplified elastic...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003513
EISBN: 978-1-62708-180-1
... r is expressed as: (Eq 12) K r = δ e δ mat + ρ where (Eq 13) δ e = K I 2 X ⋅ σ y ⋅ E ′ For plane stress and low work-hardening materials, X and E ′ are, respectively, 1 and E , while for plane strain and low work-hardening...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003546
EISBN: 978-1-62708-180-1
... and used in the analysis presented here. In planes A and B, the principal stresses along several directions (or planes) were obtained as a function of distance from the passageway bores. A typical elastic stress distribution is shown in one direction within plane A. In the analysis described here, the most...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... (see the Appendix in the article “Mechanisms and Appearances of Ductile and Brittle Fracture in Metals” in this Volume). This section describes the underlying fundamentals and the relevance and necessity of performing proper stress analysis in conducting a failure analysis. Both plane stress...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002366
EISBN: 978-1-62708-193-1
... where δ ij = 1 if i = j, 0 if i ≠ j Here, σ 1 , σ 2 , and σ 3 are the three principal stresses. The octahedral shear stress is defined as the resolved shear stress on the Π-plane, the plane making equal angles with the three principal stress directions: (Eq 1) τ oct = 1 3...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
...” in this Volume). This section describes the underlying fundamentals and the relevance and necessity of performing proper stress analysis in conducting a failure analysis. Both plane stress and plane strain are explored, and instances in which seemingly appropriate two-dimensional (2D) analyses lead...
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
.... Dislocations tend to propagate in compact atomic planes and along the shortest atomic direction. Let us denote n s the normal to the slip plane, and b s the direction of shear (Burgers vector). If σ ij is the stress tensor acting on the crystal (grain) then the resolved shear stress on the shear plane...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005131
EISBN: 978-1-62708-186-3
... has a constitutive response of σ x = E ′ε x , where E ′ is the effective modulus for the beam (plane-stress case) or E ′= E /(1−ν 2 ), where ν is Poisson's ratio, for the sheet (plane-strain case). For elastic recovery from an initially curved configuration (radius= R ) to a final...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002418
EISBN: 978-1-62708-193-1
... along the crack plane ( Ref 45 , 46 ). This zone couples the stresses and displacements into the plastic zone. All realistic rupture laws have the form depicted in Fig. 7 , characterized by a peak stress, σ*, and a dissipation, Γ*. For inelastic bridging in an elastic material, described above, σ...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005169
EISBN: 978-1-62708-186-3
... epsilon sd drawing stress ti interfacial shear (or friction) Z, f zeta sep stress at entrance to plane-strain stress H, g eta cross section tmax maximum shear stress H, h theta s1 interfacial energy per unit area of to shear yield strength I, i iota boundary W redundant work factor K, k kappa sm...