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elastic constants

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Published: 15 May 2022
Fig. 1 Spring and dashpot models. (a) Linear elastic material with constant modulus slope, E. (b) Dashpot with linear liquid viscosity slope, η. Reprinted under the Creative Commons CC BY license from Ref 1 More
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Published: 15 January 2021
Fig. 5 Results obtained from a steel four-point bend specimen in round-robin tests. The x-ray elastic constant (½ S 2 ) was determined to be 3.687 10 −5 ksi −1 . More
Image
Published: 15 May 2022
Fig. 5 Representative diagram of (a) constant stress applied to a material, and resultant (b) solid elastic strain, (c) purely viscous liquid strain, (d) viscoelastic solid strain response. The colors represent: (red) as “solid elastic” material response; (green) as “purely viscous liquid More
Image
Published: 15 May 2022
Fig. 4 Representative diagram of (a) constant strain applied to a material, and resultant (b) solid elastic stress, (c) nearly purely viscous fluid stress, and (d) viscoelastic solid stress response. The colors represent: (red) as “solid elastic” material response; (green) as “nearly purely More
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006941
EISBN: 978-1-62708-395-9
... Spring and dashpot models. (a) Linear elastic material with constant modulus slope, E. (b) Dashpot with linear liquid viscosity slope, η. Reprinted under the Creative Commons CC BY license from Ref 1 A perfectly elastic solid would follow Hooke’s Law at low strain, which, with a uniaxially...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.power.c0090114
EISBN: 978-1-62708-229-7
.... The oxidation depth is assumed to be parabolic with time, and using the Arrhenius relationship between time and temperature, that is: (Eq 1) [ log   K ⋅ log   ( d 2 / t ) ] [ T + 460 ] = Q / R where log K is constant, d is depth of the oxidation attack, t...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006934
EISBN: 978-1-62708-395-9
... of applying a constant stress to a material specimen and recording its deformation (strain) over time. When an ideal elastic solid is stressed, an immediate strain is recorded, and the applied stress, σ, is directly proportional to the strain, ε. The elastic behavior is described by the familiar Hooke...
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
... not be considered constant-volume materials. As previously indicated, constant volume corresponds to ν = 0.5. The most usual values of ν for elastic metals are between 0.25 and 0.35. If exact data are not available, a value of ν = 0.3 is typically used. Two-dimensional forms can also be given for special stress...
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
... higher compressibility and in many applications should not be considered constant volume materials. As previously indicated, constant volume corresponds to ν = 0.5. The most usual values of ν for elastic metals are between 0.25 and 0.35. If exact data are not available, a value of ν = 0.3 is typically...
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
..., during straight and level flight, aircraft jet engines have essentially constant temperatures and imposed loads, where steady-state creep (and the environment) are the primary damage mechanisms. During takeoff and landing, however, the transient demand for more power output induces load and temperature...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006781
EISBN: 978-1-62708-295-2
... plastic behavior ( Ref 11 , 12 ): (Eq 12) da dN = C Δ J q e ( − Q p RT ) Equation 11 estimates the fatigue crack growth per cycle, da / dN , as a function of material- and environmental-specific constants a and b ; the linear elastic stress-intensity factor...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006944
EISBN: 978-1-62708-395-9
... to allow the stress to decrease for the constant strain. As the temperature of amorphous thermoplastics increases, the molecular mobility increases and softening of the material occurs with an accompanying change in the elastic modulus. The effect of temperature or time on the elastic modulus...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006768
EISBN: 978-1-62708-295-2
... + σ 22 + σ 33 )         +   ½ S 2 ( σ 13 cos ϕ + σ 23 sin ϕ ) sin2 ψ where ½ S 2 and S 1 are the x-ray elastic constants of the material, variations of σ ij are the stress-tensor components, φ is the angle of the direction of strain...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006780
EISBN: 978-1-62708-295-2
... instantaneous elastic strain from the applied load, followed by a region of increasing plastic strain at a decreasing strain rate ( Fig. 3b ). Following the first stage of primary creep is the region of secondary creep, where the creep rate is nominally constant at a minimum rate, generally known as the minimum...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003528
EISBN: 978-1-62708-180-1
...-ray elastic constants of the material, variations of σ ij are the stress-tensor components, ϕ is the angle of the direction of strain measurement with respect to the frame of reference, ψ is the angle subtended by the bisector of the incident and diffracted beam, with the specimen normal, and ε ϕψ...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003545
EISBN: 978-1-62708-180-1
...) is the region of the initial instantaneous elastic strain from the applied load, followed by a region of increasing plastic strain at a decreasing strain rate ( Fig. 3b ). Following the first stage of primary creep is the region of secondary creep, where the creep rate is nominally constant at a minimum rate...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006930
EISBN: 978-1-62708-395-9
..., angular velocity On the other hand, pure deformation, which is appropriate for describing how solids behave (elastic behavior), is denoted by a spring in rheology textbooks. The behavior exhibited by solids is shown in Fig. 2 , which shows that for solids, the force exerted by the operator...
Series: ASM Failure Analysis Case Histories
Volume: 1
Publisher: ASM International
Published: 01 December 1992
DOI: 10.31399/asm.fach.v01.c9001056
EISBN: 978-1-62708-214-3
... the wall thickness, are shown in Fig. 4 . The solid lines represent these stresses once they have been transformed into elastic-plastic stresses. As can be seen in Fig. 5 , the stresses were higher than the material yield stress up to 7 mm (0.28 in.) in depth from the internal radius. Fig. 4...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
... complete application of the load is defined as one cycle. In Fig. 2 , the loading is constant amplitude because each cycle has the same load amplitude. The terms shown in this figure are defined or calculated as: Maximum stress: σ max Minimum stress: σ min Stress range: Δ...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006918
EISBN: 978-1-62708-395-9
... is the ductility coefficient, and b and c are material constants. The first term on the right side of Eq 8 is the elastic component of the strain amplitude, and the second term is the plastic component of the strain amplitude. Tests dominated by the elastic component of strain are considered high-cycle...