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conservation equations

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Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003516
EISBN: 978-1-62708-180-1
... equations or computational mechanics (finite-element analysis). One needs to know the geometries and the materials as well as the processing history and mechanical properties of the materials. Thus far, this article has briefly discussed the mechanics, the structures, and, to a lesser extent...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006823
EISBN: 978-1-62708-329-4
... is the operating pressure; r i and r o are the inside and outside tank radii, respectively; G 0 through G 4 are influence coefficients that depend on t c / r i , a /c, a / t c , ϕ, and Q and are conservatively calculated using equations given in paragraphs 9B.5.10 and 9B.14.3 and Table 9B.13...
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
... sign. Contemporary models to predict plastic deformation utilize the “flow” (i.e., yield) surface via the plastic potential equation. Because any linear model to predict flow (e.g., the Tresca criterion) is discontinuous in principal stress space, it cannot predict plastic strains for several loading...
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
..., and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear...
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
... for calculating the remaining life. This assumption leads to conservative results, desirable in such applications. For other types of cracks, the ligament size is assumed to be the final crack size. Remaining Life Calculation The equation governing the fatigue crack growth behavior as a function of hold...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.usage.c9001672
EISBN: 978-1-62708-236-5
... mechanics calculation. The critical stress intensity factor, K IIIc , was determined using the maximum shear stress developed at failure and this equation: (Eq 4) K IIIc = 0.41   T f / γ   2.5 utilized by Shah [ 4 ], where T f is torque at fracture and r is specimen radius...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006921
EISBN: 978-1-62708-395-9
... in environment between the test group and actual field service, and testing at a temperature that changes the properties and behavior of the plastic so drastically that extrapolation to actual use temperatures is not valid. Generally, accelerated test conditions are selected to represent a conservative estimate...
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
.... Elevated-temperature-assisted inelastic deformation may occur by discrete obstacle resistance to dislocation motion, lattice resistance to dislocation motion, or twinning, as in the example in Ref 2 . Twinning will be omitted from the discussion here. The rate equations for temperature-assisted inelastic...
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
...: σ a S e + σ m σ f = 1 Fig. 6 Comparison of mean stress equations from (a) Soderberg, (b) Goodman, (c) Gerber, and (d) Morrow. Adapted from Ref 6 Fatigue Damage Summation The Palmgren-Miner damage summation rule ( Ref 32 – 34 ), sometimes referred...
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
... equation: (Eq 1) σ = E ε where E is the modulus of elasticity ( Fig. 1a ). Fig. 1 Creep-recovery response of (a) Hookean model and (b) Newtonian model On the other hand, the deformation of an ideal viscous material occurs as the stress is maintained. In this case, the strain...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006929
EISBN: 978-1-62708-395-9
... Abstract This article provides an overview of the physics and math associated with moisture-related failures in plastic components. It develops key equations, showing how they are used to analyze the causes and effects of water uptake, diffusion, and moisture concentration in polymeric...
Series: ASM Failure Analysis Case Histories
Volume: 2
Publisher: ASM International
Published: 01 December 1993
DOI: 10.31399/asm.fach.v02.c9001272
EISBN: 978-1-62708-215-0
..., at this stress level, fracture mechanics indicated that the 25 mm (1 in.) starter crack exceeded or was very near the critical crack length for the material. Additional factors not taken into account in the design equations included cold work from a hole punching operation, thread imprinting in bolt holes...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.petrol.c9001137
EISBN: 978-1-62708-228-0
... type and heat treatment as used in the earlier fitness for purpose already been measured, at its operating temperature of −130°C to be δ i = 0.05 ±0.02 mm (for conservatism reasons the COD at crack initiation δ i , was employed rather than the less conservative, but now widely accepted ( 5 ), COD...
Series: ASM Failure Analysis Case Histories
Volume: 1
Publisher: ASM International
Published: 01 December 1992
DOI: 10.31399/asm.fach.v01.c9001114
EISBN: 978-1-62708-214-3
...—qualitative evidence that general yielding did not occur prior to failure. To obtain a more quantitative estimate of the stress at the time of failure, a simplistic fracture mechanics analysis was performed. From equations such as the one given below ( Ref 1 ), K Ic can be estimated: (Eq 1) K Ic...
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
... from expressions for J -integrals from the EPRI/GE handbook ( Ref 4 ) reformulated to use actual true stress-strain curves. Also, approximations erring on the conservative side were introduced to make the formulae geometrically independent, thus obviating the need for fully plastic power-law solutions...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.chem.c9001738
EISBN: 978-1-62708-220-4
... view, this will be on the conservative side because of the upperbound stress value chosen. The secondary creep rate at the service temperature can be obtained by extrapolation from the iso-stress testing results at higher temperatures; see figure 7 . At 800°C a creep rate of 2.5 · 10 −4 %/hr...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006807
EISBN: 978-1-62708-329-4
... of heater tubes operating in the creep range ( Ref 11 , 12 ). The LMP was developed in the early 1950s based on the observation that the creep rate follows an Arrhenius-type equation. The concept behind the LMP approach is shown graphically in Fig. 3 . In this method, a number of tests are carried out...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003517
EISBN: 978-1-62708-180-1
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... (or reliability) analysis depends on the number of failure equations required to describe the structural behavior. A system reliability analysis is required if a structure is composed of multiple components, has multiple failure modes, and/or has multiple failure locations, for example, multi-site damage. In each...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001781
EISBN: 978-1-62708-241-9
... of the shaft, and I is the moment of inertia. This equation sets an upper bound for the ultimate stress, which was calculated as 389.74 MPa. Secondly, assuming an elastic-perfectly plastic material model, failure occurs once all the material has reached the ultimate stress. To calculate the failure...